diff --git a/mediapipe/framework/input_stream_handler.cc b/mediapipe/framework/input_stream_handler.cc
index d1dffa41..a7bd9ef4 100644
--- a/mediapipe/framework/input_stream_handler.cc
+++ b/mediapipe/framework/input_stream_handler.cc
@@ -354,7 +354,9 @@ NodeReadiness SyncSet::GetReadiness(Timestamp* min_stream_timestamp) {
     }
   }
   *min_stream_timestamp = std::min(min_packet, min_bound);
-  if (*min_stream_timestamp == Timestamp::Done()) {
+  if (*min_stream_timestamp >= Timestamp::OneOverPostStream()) {
+    // Either OneOverPostStream or Done indicates no more packets.
+    *min_stream_timestamp = Timestamp::Done();
     last_processed_ts_ = Timestamp::Done().PreviousAllowedInStream();
     return NodeReadiness::kReadyForClose;
   }
diff --git a/mediapipe/framework/stream_handler/immediate_input_stream_handler_test.cc b/mediapipe/framework/stream_handler/immediate_input_stream_handler_test.cc
index e721afb0..e5de7f0c 100644
--- a/mediapipe/framework/stream_handler/immediate_input_stream_handler_test.cc
+++ b/mediapipe/framework/stream_handler/immediate_input_stream_handler_test.cc
@@ -230,6 +230,43 @@ TEST_F(ImmediateInputStreamHandlerTest, StreamDoneReady) {
   input_stream_handler_->ClearCurrentInputs(cc_);
 }
 
+// This test checks that the state is ReadyForClose after all streams reach
+// Timestamp::Max.
+TEST_F(ImmediateInputStreamHandlerTest, ReadyForCloseAfterTimestampMax) {
+  Timestamp min_stream_timestamp;
+  std::list<Packet> packets;
+
+  // One packet arrives, ready for process.
+  packets.push_back(Adopt(new std::string("packet 1")).At(Timestamp(10)));
+  input_stream_handler_->AddPackets(name_to_id_["input_a"], packets);
+  EXPECT_TRUE(input_stream_handler_->ScheduleInvocations(
+      /*max_allowance=*/1, &min_stream_timestamp));
+  EXPECT_EQ(Timestamp(10), cc_->InputTimestamp());
+  input_stream_handler_->FinalizeInputSet(cc_->InputTimestamp(),
+                                          &cc_->Inputs());
+  input_stream_handler_->ClearCurrentInputs(cc_);
+
+  // No packets arrive, not ready.
+  EXPECT_FALSE(input_stream_handler_->ScheduleInvocations(
+      /*max_allowance=*/1, &min_stream_timestamp));
+  EXPECT_EQ(Timestamp::Unset(), cc_->InputTimestamp());
+
+  // Timestamp::Max arrives, ready for close.
+  input_stream_handler_->SetNextTimestampBound(
+      name_to_id_["input_a"], Timestamp::Max().NextAllowedInStream());
+  input_stream_handler_->SetNextTimestampBound(
+      name_to_id_["input_b"], Timestamp::Max().NextAllowedInStream());
+  input_stream_handler_->SetNextTimestampBound(
+      name_to_id_["input_c"], Timestamp::Max().NextAllowedInStream());
+
+  EXPECT_TRUE(input_stream_handler_->ScheduleInvocations(
+      /*max_allowance=*/1, &min_stream_timestamp));
+  EXPECT_EQ(Timestamp::Done(), cc_->InputTimestamp());
+  input_stream_handler_->FinalizeInputSet(cc_->InputTimestamp(),
+                                          &cc_->Inputs());
+  input_stream_handler_->ClearCurrentInputs(cc_);
+}
+
 // This test checks that when any stream is done, the state is ready to close.
 TEST_F(ImmediateInputStreamHandlerTest, ReadyForClose) {
   Timestamp min_stream_timestamp;