diff --git a/src/Timer.cc b/src/Timer.cc
index b6d6100e7f..77d74fcdbb 100644
--- a/src/Timer.cc
+++ b/src/Timer.cc
@@ -93,7 +93,7 @@ void TimerMgr::Process()
 	// pseudo-realtime), advance the timer here to the current time since otherwise it won't
 	// move forward and the timers won't fire correctly.
 	iosource::PktSrc* pkt_src = iosource_mgr->GetPktSrc();
-	if ( ! pkt_src || ! pkt_src->IsOpen() || reading_live )
+	if ( ! pkt_src || ! pkt_src->IsOpen() || reading_live || net_is_processing_suspended() )
 		net_update_time(current_time());
 
 	// Just advance the timer manager based on the current network time. This won't actually
diff --git a/src/iosource/Manager.cc b/src/iosource/Manager.cc
index 57f3caecdf..6ffc924ab8 100644
--- a/src/iosource/Manager.cc
+++ b/src/iosource/Manager.cc
@@ -167,7 +167,7 @@ void Manager::FindReadySources(std::vector<IOSource*>* ready)
 				else
 					{
 					if ( ! pseudo_realtime )
-						// A pcap file is always ready to process.
+						// A pcap file is always ready to process unless it's suspended
 						ready->push_back(pkt_src);
 					}
 				}
diff --git a/testing/btest/Baseline/core.pcap.suspend-processing/.stderr b/testing/btest/Baseline/core.pcap.suspend-processing/.stderr
new file mode 100644
index 0000000000..7998283271
--- /dev/null
+++ b/testing/btest/Baseline/core.pcap.suspend-processing/.stderr
@@ -0,0 +1,3 @@
+1300475167.096535 processing suspended
+1588361692.527039 processing continued
+1588361692.527039 received termination signal
diff --git a/testing/btest/Baseline/core.pcap.suspend-processing/output b/testing/btest/Baseline/core.pcap.suspend-processing/output
new file mode 100644
index 0000000000..a83400f0e7
--- /dev/null
+++ b/testing/btest/Baseline/core.pcap.suspend-processing/output
@@ -0,0 +1,22 @@
+network_time: 1300475167.096535
+Processing packet 1 at 1300475167.096535
+network_time: 1588361692.527039
+Processing packet 2 at 1588361692.527039
+Processing packet 3 at 1588361692.527039
+Processing packet 4 at 1588361692.527039
+Processing packet 5 at 1588361692.527039
+Processing packet 6 at 1588361692.527039
+Processing packet 7 at 1588361692.527039
+Processing packet 8 at 1588361692.527039
+Processing packet 9 at 1588361692.527039
+Processing packet 10 at 1588361692.527039
+Processing packet 11 at 1588361692.527039
+Processing packet 12 at 1588361692.527039
+Processing packet 13 at 1588361692.527039
+Processing packet 14 at 1588361692.527039
+Processing packet 15 at 1588361692.527039
+Processing packet 16 at 1588361692.527039
+Processing packet 17 at 1588361692.527039
+Processing packet 18 at 1588361692.527039
+Processing packet 19 at 1588361692.527039
+Processing packet 20 at 1588361692.527039
diff --git a/testing/btest/core/pcap/suspend-processing.zeek b/testing/btest/core/pcap/suspend-processing.zeek
new file mode 100644
index 0000000000..fb56bbb75e
--- /dev/null
+++ b/testing/btest/core/pcap/suspend-processing.zeek
@@ -0,0 +1,34 @@
+# @TEST-EXEC: zeek -C -r $TRACES/wikipedia.trace %INPUT >output
+# @TEST-EXEC: btest-diff output
+# @TEST-EXEC: btest-diff .stderr
+
+redef exit_only_after_terminate = T;
+
+event go_on()
+	{
+	continue_processing();
+	print fmt("network_time: %f", network_time());
+	}
+
+event pcap_init()
+	{
+	print fmt("network_time: %f", network_time());
+	suspend_processing();
+	# Some asynchronous work
+	schedule 5sec { go_on() };
+	}
+
+event zeek_init()
+	{
+	schedule 0sec { pcap_init() };
+	}
+
+global pkt_cnt: count = 0;
+
+event new_packet(c: connection, p: pkt_hdr)
+	{
+	pkt_cnt += 1;
+	print fmt("Processing packet %s at %f", pkt_cnt, network_time());
+	if ( pkt_cnt >= 20 )
+		terminate();
+	}