diff --git a/sdk/span.go b/sdk/span.go
index fc143d0ad..707fc0fe6 100644
--- a/sdk/span.go
+++ b/sdk/span.go
@@ -367,10 +367,22 @@ func (s *span) AddLink(link trace.Link) {
 		return
 	}
 
+	l := maxSpan.Links
+
 	s.mu.Lock()
 	defer s.mu.Unlock()
 
-	// TODO: handle link limits.
+	if l == 0 {
+		s.span.DroppedLinks++
+		return
+	}
+
+	if l > 0 && len(s.span.Links) == l {
+		// Drop head while avoiding allocation of more capacity.
+		copy(s.span.Links[:l-1], s.span.Links[1:])
+		s.span.Links = s.span.Links[:l-1]
+		s.span.DroppedLinks++
+	}
 
 	s.span.Links = append(s.span.Links, convLink(link))
 }
@@ -384,13 +396,20 @@ func convLinks(links []trace.Link) []*telemetry.SpanLink {
 }
 
 func convLink(link trace.Link) *telemetry.SpanLink {
-	return &telemetry.SpanLink{
+	l := &telemetry.SpanLink{
 		TraceID:    telemetry.TraceID(link.SpanContext.TraceID()),
 		SpanID:     telemetry.SpanID(link.SpanContext.SpanID()),
 		TraceState: link.SpanContext.TraceState().String(),
-		Attrs:      convAttrs(link.Attributes),
 		Flags:      uint32(link.SpanContext.TraceFlags()),
 	}
+
+	limit := maxSpan.LinkAttrs
+
+	var dropped int
+	l.Attrs, dropped = convCappedAttrs(limit, link.Attributes)
+	l.DroppedAttrs += uint32(dropped)
+
+	return l
 }
 
 func (s *span) SetName(name string) {
diff --git a/sdk/span_test.go b/sdk/span_test.go
index 7090e3fd9..7098a876e 100644
--- a/sdk/span_test.go
+++ b/sdk/span_test.go
@@ -345,13 +345,41 @@ func TestSpanNilUnsampledGuards(t *testing.T) {
 }
 
 func TestSpanAddLink(t *testing.T) {
+	t.Setenv("OTEL_LINK_ATTRIBUTE_COUNT_LIMIT", "1")
+	t.Setenv("OTEL_SPAN_LINK_COUNT_LIMIT", "3")
+	t.Cleanup(resetMaxSpan())
+
 	s := spanBuilder{
 		Options: []trace.SpanStartOption{trace.WithLinks(link0)},
 	}.Build()
 	s.AddLink(link1)
 
 	want := []*telemetry.SpanLink{tLink0, tLink1}
-	assert.Equal(t, want, s.span.Links)
+	if !assert.Equal(t, want, s.span.Links) {
+		// Reset for next part of test.
+		want = s.span.Links
+	}
+
+	s.AddLink(trace.Link{
+		Attributes: []attribute.KeyValue{
+			attribute.Int("one", 1),
+			attribute.Int("two", 2),
+		},
+	})
+
+	want = append(want, &telemetry.SpanLink{
+		Attrs:        []telemetry.Attr{telemetry.Int("one", 1)},
+		DroppedAttrs: 1,
+	})
+	if !assert.Equal(t, want, s.span.Links, "attribute limit") {
+		// Reset for next part of test.
+		want = s.span.Links
+	}
+
+	s.AddLink(trace.Link{})
+	want = append(want[1:], new(telemetry.SpanLink))
+	assert.Equal(t, want, s.span.Links, "link limit")
+	assert.Equal(t, uint32(1), s.span.DroppedLinks)
 }
 
 func TestSpanIsRecording(t *testing.T) {