diff --git a/tools/valgrind-webrtc/memcheck/suppressions.txt b/tools/valgrind-webrtc/memcheck/suppressions.txt
index 2af0e91b76..a55ac1ba8e 100644
--- a/tools/valgrind-webrtc/memcheck/suppressions.txt
+++ b/tools/valgrind-webrtc/memcheck/suppressions.txt
@@ -369,6 +369,29 @@
 
 #-----------------------------------------------------------------------
 # 2. libjingle stuff (talk folder)
+{
+   bug_1976_1
+   Memcheck:Unaddressable
+   fun:pthread_mutex_unlock
+   fun:_ZN9talk_base15CriticalSection5LeaveEv
+   fun:_ZN9talk_base9CritScopeD1Ev
+   ...
+   fun:_ZN9talk_base6Thread15ProcessMessagesEi
+   fun:_ZN9talk_base6Thread3RunEv
+   fun:_ZN9talk_base6Thread6PreRunEPv
+}
+{
+   bug_1976_2
+   Memcheck:Leak
+   fun:calloc
+   obj:/usr/lib/x86_64-linux-gnu/libnss3.so
+   ...
+   fun:NSS_NoDB_Init
+   fun:_ZN9talk_base10NSSContext13InitializeSSLEPFbPvE
+   fun:_ZN9talk_base13InitializeSSLEPFbPvE
+   fun:_ZN9talk_base10RandomTest13SetUpTestCaseEv
+   fun:_ZN7testing8TestCase16RunSetUpTestCaseEv
+}
 {
    bug_2056_1
    Memcheck:Leak
diff --git a/tools/valgrind-webrtc/tsan/suppressions.txt b/tools/valgrind-webrtc/tsan/suppressions.txt
index cb1cb4b69f..612af305c6 100644
--- a/tools/valgrind-webrtc/tsan/suppressions.txt
+++ b/tools/valgrind-webrtc/tsan/suppressions.txt
@@ -727,3 +727,26 @@
   fun:talk_base::Thread::Run
   fun:talk_base::Thread::PreRun
 }
+{
+  bug_2080_35
+  ThreadSanitizer:UnlockNonLocked
+  fun:pthread_mutex_unlock
+  fun:talk_base::CriticalSection::Leave
+  fun:talk_base::CritScope::~CritScope
+  ...
+  fun:talk_base::AsyncFunctorMessageHandler::OnMessage
+  fun:talk_base::MessageQueue::Dispatch
+  fun:talk_base::Thread::ProcessMessages
+  fun:talk_base::Thread::Run
+  fun:talk_base::Thread::PreRun
+}
+{
+  bug_2080_36
+  ThreadSanitizer:Race
+  ...
+  fun:talk_base::FunctorMessageHandler::OnMessage
+  fun:talk_base::MessageQueue::Dispatch
+  fun:talk_base::Thread::ProcessMessages
+  fun:talk_base::Thread::Run
+  fun:talk_base::Thread::PreRun
+}