diff --git a/.travis.yml b/.travis.yml
index 490b3bb..9d1cb69 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -47,14 +47,20 @@ jobs:
     - dist: xenial
       compiler: clang
       arch: arm64
+      # ASAN fails with internal error
+      env: DISABLE_ASAN=1
 
     - dist: xenial
       compiler: gcc
       arch: ppc64le
+      # ASAN fails with internal error
+      env: DISABLE_ASAN=1
 
     - dist: xenial
       compiler: clang
       arch: ppc64le
+      # ASAN fails with internal error
+      env: DISABLE_ASAN=1
 
     - dist: xenial
       compiler: gcc
diff --git a/scripts/run_tests.sh b/scripts/run_tests.sh
index 482565d..0e1b3be 100755
--- a/scripts/run_tests.sh
+++ b/scripts/run_tests.sh
@@ -35,6 +35,13 @@ CC_VERSION=$($CC --version | head -1)
 
 ARCH=$(uname -m)
 
+# Allow setting DISABLE_ASAN=1 in the environment to disable the ASAN tests.
+if [ "${DISABLE_ASAN:-}" = "1" ]; then
+	DISABLE_ASAN=true
+else
+	DISABLE_ASAN=false
+fi
+
 ###############################################################################
 
 INDENT=0
@@ -250,6 +257,17 @@ run_tests() {
 		log "Skipping UBSAN tests because compiler ($CC_VERSION) doesn't support UBSAN"
 	fi
 
+	cflags=("-fsanitize=address" "-fno-sanitize-recover=address")
+	if $DISABLE_ASAN; then
+		log "Skipping ASAN tests because DISABLE_ASAN=1 was set"
+	elif cflags_supported "${cflags[@]}"; then
+		begin "Running tests with ASAN"
+		CFLAGS="$CFLAGS ${cflags[*]}" do_run_tests --quick
+		end
+	else
+		log "Skipping ASAN tests because compiler ($CC_VERSION) doesn't support ASAN"
+	fi
+
 	install_uninstall_tests
 	check_symbol_prefixes
 }