diff --git a/interpreter/operator_dispatcher.go b/interpreter/operator_dispatcher.go
index af782da..a2f165d 100644
--- a/interpreter/operator_dispatcher.go
+++ b/interpreter/operator_dispatcher.go
@@ -1246,6 +1246,34 @@ func (i *interpreter) binaryOverloads(m model.IBinaryExpression) ([]convert.Over
 				Operands: []types.IType{&types.List{ElementType: types.Any}, &types.List{ElementType: types.Any}},
 				Result:   evalProperlyIncludedInList,
 			},
+			{
+				Operands: []types.IType{&types.Interval{PointType: types.Date}, &types.Interval{PointType: types.Date}},
+				Result:   i.evalProperlyIncludedInInterval,
+			},
+			{
+				Operands: []types.IType{&types.Interval{PointType: types.DateTime}, &types.Interval{PointType: types.DateTime}},
+				Result:   i.evalProperlyIncludedInInterval,
+			},
+			{
+				Operands: []types.IType{&types.Interval{PointType: types.Integer}, &types.Interval{PointType: types.Integer}},
+				Result:   i.evalProperlyIncludedInInterval,
+			},
+			{
+				Operands: []types.IType{&types.Interval{PointType: types.Long}, &types.Interval{PointType: types.Long}},
+				Result:   i.evalProperlyIncludedInInterval,
+			},
+			{
+				Operands: []types.IType{&types.Interval{PointType: types.Decimal}, &types.Interval{PointType: types.Decimal}},
+				Result:   i.evalProperlyIncludedInInterval,
+			},
+			{
+				Operands: []types.IType{&types.Interval{PointType: types.Quantity}, &types.Interval{PointType: types.Quantity}},
+				Result:   i.evalProperlyIncludedInInterval,
+			},
+			{
+				Operands: []types.IType{&types.Interval{PointType: types.Time}, &types.Interval{PointType: types.Time}},
+				Result:   i.evalProperlyIncludedInInterval,
+			},
 		}, nil
 	case *model.Skip:
 		return []convert.Overload[evalBinarySignature]{
diff --git a/interpreter/operator_interval.go b/interpreter/operator_interval.go
index e0461dc..ef09b1b 100644
--- a/interpreter/operator_interval.go
+++ b/interpreter/operator_interval.go
@@ -15,6 +15,7 @@
 package interpreter
 
 import (
+	"cmp"
 	"fmt"
 	"time"
 
@@ -641,3 +642,109 @@ func evalWidthInterval(m model.IUnaryExpression, intervalObj result.Value) (resu
 	}
 	return result.Value{}, fmt.Errorf("internal error - unsupported point type in evalWidthInterval: %v", start.RuntimeType())
 }
+
+// ProperlyIncludedIn(left Interval<T>, right Interval<T>) Boolean
+// https://cql.hl7.org/09-b-cqlreference.html#properly-included-in-1
+func (i *interpreter) evalProperlyIncludedInInterval(b model.IBinaryExpression, lObj, rObj result.Value) (result.Value, error) {
+	if result.IsNull(lObj) || result.IsNull(rObj) {
+		return result.New(nil)
+	}
+	if m, ok := b.(*model.ProperlyIncludedIn); ok && m.Precision != model.UNSETDATETIMEPRECISION {
+		return result.Value{}, fmt.Errorf("internal error - properly included in does not yet support precision")
+	}
+
+	// start and end handle null inclusivity and open boundaries, so every bound below is closed and
+	// a null bound is unknown.
+	leftStart, leftEnd, err := startAndEnd(lObj, &i.evaluationTimestamp)
+	if err != nil {
+		return result.Value{}, err
+	}
+	rightStart, rightEnd, err := startAndEnd(rObj, &i.evaluationTimestamp)
+	if err != nil {
+		return result.Value{}, err
+	}
+
+	startComp, err := compareIntervalPoints(leftStart, rightStart)
+	if err != nil {
+		return result.Value{}, err
+	}
+	endComp, err := compareIntervalPoints(leftEnd, rightEnd)
+	if err != nil {
+		return result.Value{}, err
+	}
+	if startComp == leftBeforeRight || endComp == leftAfterRight {
+		return result.New(false)
+	}
+
+	// An unknown start is at most the left end and an unknown end is at least the left start, so
+	// Interval(null, 1] properly included in Interval[5, null) is still false.
+	if result.IsNull(leftStart) {
+		c, err := compareIntervalPoints(leftEnd, rightStart)
+		if err != nil {
+			return result.Value{}, err
+		}
+		if c == leftBeforeRight {
+			return result.New(false)
+		}
+	}
+	if result.IsNull(leftEnd) {
+		c, err := compareIntervalPoints(leftStart, rightEnd)
+		if err != nil {
+			return result.Value{}, err
+		}
+		if c == leftAfterRight {
+			return result.New(false)
+		}
+	}
+
+	startKnown := startComp == leftEqualRight || startComp == leftAfterRight
+	endKnown := endComp == leftEqualRight || endComp == leftBeforeRight
+	if !startKnown || !endKnown {
+		return result.New(nil)
+	}
+	return result.New(startComp == leftAfterRight || endComp == leftBeforeRight)
+}
+
+// compareIntervalPoints compares two interval points of the same point type. It returns
+// comparedToNull if either point is null or if Quantity units cannot be converted.
+func compareIntervalPoints(l, r result.Value) (comparison, error) {
+	if result.IsNull(l) || result.IsNull(r) {
+		return comparedToNull, nil
+	}
+	switch l.RuntimeType() {
+	case types.Integer:
+		return compareValues(l, r, result.ToInt32)
+	case types.Long:
+		return compareValues(l, r, result.ToInt64)
+	case types.Decimal:
+		return compareValues(l, r, result.ToFloat64)
+	case types.Quantity:
+		lq, rq, err := applyToValues(l, r, result.ToQuantity)
+		if err != nil {
+			return unsetComparison, err
+		}
+		if lq.Unit == rq.Unit {
+			return toComparison(cmp.Compare(lq.Value, rq.Value)), nil
+		}
+		converted, err := ucum.ConvertUnit(lq.Value, string(lq.Unit), string(rq.Unit))
+		if err != nil {
+			return comparedToNull, nil
+		}
+		return toComparison(cmp.Compare(converted, rq.Value)), nil
+	case types.Date, types.DateTime, types.Time:
+		ldt, rdt, err := applyToValues(l, r, result.ToDateTime)
+		if err != nil {
+			return unsetComparison, err
+		}
+		return compareDateTime(ldt, rdt)
+	}
+	return unsetComparison, fmt.Errorf("internal error - unsupported point type in compareIntervalPoints: %v", l.RuntimeType())
+}
+
+func compareValues[t cmp.Ordered](l, r result.Value, fn func(result.Value) (t, error)) (comparison, error) {
+	lv, rv, err := applyToValues(l, r, fn)
+	if err != nil {
+		return unsetComparison, err
+	}
+	return toComparison(cmp.Compare(lv, rv)), nil
+}
diff --git a/parser/operators.go b/parser/operators.go
index 1f616c2..50efab7 100644
--- a/parser/operators.go
+++ b/parser/operators.go
@@ -1871,6 +1871,13 @@ func (p *Parser) loadSystemOperators() error {
 			operands: [][]types.IType{
 				{convert.GenericType, convert.GenericList},
 				{convert.GenericList, convert.GenericList},
+				{&types.Interval{PointType: types.Date}, &types.Interval{PointType: types.Date}},
+				{&types.Interval{PointType: types.DateTime}, &types.Interval{PointType: types.DateTime}},
+				{&types.Interval{PointType: types.Integer}, &types.Interval{PointType: types.Integer}},
+				{&types.Interval{PointType: types.Long}, &types.Interval{PointType: types.Long}},
+				{&types.Interval{PointType: types.Decimal}, &types.Interval{PointType: types.Decimal}},
+				{&types.Interval{PointType: types.Quantity}, &types.Interval{PointType: types.Quantity}},
+				{&types.Interval{PointType: types.Time}, &types.Interval{PointType: types.Time}},
 			},
 			model: func() model.IExpression {
 				return &model.ProperlyIncludedIn{
diff --git a/tests/enginetests/operator_interval_test.go b/tests/enginetests/operator_interval_test.go
index 595a902..dc0aca3 100644
--- a/tests/enginetests/operator_interval_test.go
+++ b/tests/enginetests/operator_interval_test.go
@@ -125,6 +125,137 @@ func TestEnd(t *testing.T) {
 	}
 }
 
+func TestProperlyIncludedInInterval(t *testing.T) {
+	tests := []struct {
+		name string
+		cql  string
+		want result.Value
+	}{
+		{
+			name: "Properly included Date intervals",
+			cql:  `Interval[@2020-01-05, @2020-01-15] properly included in Interval[@2020-01-01, @2020-01-20]`,
+			want: newOrFatal(t, true),
+		},
+		{
+			name: "Equal Date intervals not properly included",
+			cql:  `Interval[@2020-01-01, @2020-01-15] properly included in Interval[@2020-01-01, @2020-01-15]`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Not included Date intervals",
+			cql:  `Interval[@2020-01-01, @2020-01-25] properly included in Interval[@2020-01-05, @2020-01-15]`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Properly included Integer intervals",
+			cql:  `Interval[5, 15] properly included in Interval[1, 20]`,
+			want: newOrFatal(t, true),
+		},
+		{
+			name: "Equal Integer intervals not properly included",
+			cql:  `Interval[1, 15] properly included in Interval[1, 15]`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Not included Integer intervals",
+			cql:  `Interval[1, 25] properly included in Interval[5, 15]`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Null left interval",
+			cql:  `(null as Interval<Date>) properly included in Interval[@2020-01-01, @2020-01-15]`,
+			want: newOrFatal(t, nil),
+		},
+		{
+			name: "Null right interval",
+			cql:  `Interval[@2020-01-01, @2020-01-15] properly included in (null as Interval<Date>)`,
+			want: newOrFatal(t, nil),
+		},
+		{
+			name: "Unknown left start ends before right start",
+			cql:  `Interval(null, 1] properly included in Interval[5, null)`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Unknown left end starts after right end",
+			cql:  `Interval[5, null) properly included in Interval(null, 1]`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Unknown left start inside right interval",
+			cql:  `Interval(null, 5] properly included in Interval[1, 10]`,
+			want: newOrFatal(t, nil),
+		},
+		{
+			name: "Unknown right start",
+			cql:  `Interval[2, 5] properly included in Interval(null, 10]`,
+			want: newOrFatal(t, nil),
+		},
+		{
+			name: "Closed null right bounds",
+			cql:  `Interval[2, 5] properly included in Interval[null as Integer, null as Integer]`,
+			want: newOrFatal(t, true),
+		},
+		{
+			name: "Same Integer interval with different boundary inclusivity",
+			cql:  `Interval[1, 5] properly included in Interval[1, 6)`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Properly included Long intervals",
+			cql:  `Interval[2L, 4L] properly included in Interval[1L, 5L]`,
+			want: newOrFatal(t, true),
+		},
+		{
+			name: "Properly included Decimal intervals with open bounds",
+			cql:  `Interval(1.0, 2.0) properly included in Interval[1.0, 2.0]`,
+			want: newOrFatal(t, true),
+		},
+		{
+			name: "Properly included Time intervals",
+			cql:  `Interval[@T10:00, @T11:00] properly included in Interval[@T09:00, @T12:00]`,
+			want: newOrFatal(t, true),
+		},
+		{
+			name: "Date intervals with insufficient precision",
+			cql:  `Interval[@2020, @2021] properly included in Interval[@2020-01-01, @2022-01-01]`,
+			want: newOrFatal(t, nil),
+		},
+		{
+			name: "Quantity intervals with convertible units",
+			cql:  `Interval[500 'g', 900 'g'] properly included in Interval[0.1 'kg', 1 'kg']`,
+			want: newOrFatal(t, true),
+		},
+		{
+			name: "Same Quantity interval in different units",
+			cql:  `Interval[1 'kg', 2 'kg'] properly included in Interval[1000 'g', 2000 'g']`,
+			want: newOrFatal(t, false),
+		},
+		{
+			name: "Quantity intervals with incompatible units",
+			cql:  `Interval[1 'g', 2 'g'] properly included in Interval[1 'm', 5 'm']`,
+			want: newOrFatal(t, nil),
+		},
+	}
+
+	for _, tc := range tests {
+		t.Run(tc.name, func(t *testing.T) {
+			p := newFHIRParser(t)
+			parsedLibs, err := p.Libraries(context.Background(), wrapInLib(t, tc.cql), parser.Config{})
+			if err != nil {
+				t.Fatalf("Parse returned unexpected error: %v", err)
+			}
+			results, err := interpreter.Eval(context.Background(), parsedLibs, defaultInterpreterConfig(t, p))
+			if err != nil {
+				t.Fatalf("Eval returned unexpected error: %v", err)
+			}
+			if diff := cmp.Diff(tc.want, getTESTRESULT(t, results), protocmp.Transform()); diff != "" {
+				t.Errorf("Evaluate diff (-want +got):\n%s", diff)
+			}
+		})
+	}
+}
+
 func TestStart(t *testing.T) {
 	tests := []struct {
 		name       string
diff --git a/tests/spectests/exclusions/exclusions.go b/tests/spectests/exclusions/exclusions.go
index 50d255e..28204e8 100644
--- a/tests/spectests/exclusions/exclusions.go
+++ b/tests/spectests/exclusions/exclusions.go
@@ -235,7 +235,6 @@ func XMLTestFileExclusionDefinitions() map[string]XMLTestFileExclusions {
 				"ProperContains",
 				"ProperIn",
 				"ProperlyIncludes",
-				"ProperlyIncludedIn",
 				"Starts",
 				"Union",
 			},
@@ -311,6 +310,7 @@ func XMLTestFileExclusionDefinitions() map[string]XMLTestFileExclusions {
 				// TODO: b/342064453 - Ambiguous match.
 				"TestEqualNull",
 				"TestInNullBoundaries",
+				"IntegerIntervalProperlyIncludedInNullBoundaries",
 			},
 		},
 		"CqlListOperatorsTest.xml": {