Index: utils/lit/lit/run.py
===================================================================
--- utils/lit/lit/run.py
+++ utils/lit/lit/run.py
@@ -1,4 +1,5 @@
 import os
+import math
 import sys
 import threading
 import time
@@ -93,6 +94,17 @@
             for a in async_results:
                 if deadline:
                     a.wait(deadline - time.time())
+                    if not a.ready():
+                        # We reached the deadline
+                        assert time.time() >= deadline
+                        self.notify_max_total_time_reached()
+                        # FIXME: We should find a way to find the currently
+                        # running tests and mark them as TIMEOUT. Right now
+                        # because they don't get proceessed they get marked as
+                        # UNRESOLVED which is wrong.
+                        pool.terminate()
+                        pool.join()
+                        break
                 else:
                     # Python condition variables cannot be interrupted unless
                     # they have a timeout. This can make lit unresponsive to
@@ -111,6 +123,52 @@
         finally:
             pool.join()
 
+    def execute_tests_sequentially_in_process(self, max_time):
+        deadline = None
+        if max_time:
+            deadline = time.time() + max_time
+
+        # `worker_run_one_test()` currently requires the `child_lit_config`
+        # global to be set up.
+        global child_lit_config
+        child_lit_config = self.lit_config
+
+        # Execute tests sequentially.
+        for test_index, test in enumerate(self.tests):
+            if max_time is not None:
+                # FIXME: This is a hack. We set the per test timeout to be the
+                # minimum of the remaining time to the deadline and the current
+                # timeout value.  This is only safe to do because we are
+                # running tests sequentially, and so modifying the global
+                # lit_config object is fine.
+                #
+                # Using `maxIndividualTestTime` means we inherit its dependencies.
+                # This means that we need Python's `psutil` in order for this to work
+                # right now.
+                remaining_time = int(math.ceil(deadline - time.time()))
+                if remaining_time <= 0:
+                    self.notify_max_total_time_reached()
+                    break
+                if self.lit_config.maxIndividualTestTime > 0:
+                    self.lit_config.maxIndividualTestTime = min(
+                        self.lit_config.maxIndividualTestTime,
+                        remaining_time
+                    )
+                else:
+                    self.lit_config.maxIndividualTestTime = remaining_time
+            result = worker_run_one_test(test_index, test)
+            self.consume_test_result(result)
+            if max_time is not None:
+                if time.time() >= deadline:
+                    self.notify_max_total_time_reached()
+                    break
+
+    def notify_max_total_time_reached(self):
+        self.lit_config.warning(
+            'Used up max time. '
+            'Not running any more tests'
+        )
+
     def execute_tests(self, display, jobs, max_time=None):
         """
         execute_tests(display, jobs, [max_time])
@@ -143,11 +201,7 @@
         self.failure_count = 0
         self.hit_max_failures = False
         if self.lit_config.singleProcess:
-            global child_lit_config
-            child_lit_config = self.lit_config
-            for test_index, test in enumerate(self.tests):
-                result = worker_run_one_test(test_index, test)
-                self.consume_test_result(result)
+            self.execute_tests_sequentially_in_process(max_time)
         else:
             self.execute_tests_in_pool(jobs, max_time)
 
Index: utils/lit/tests/Inputs/shtest-max-global-time/0_short.py
===================================================================
--- /dev/null
+++ utils/lit/tests/Inputs/shtest-max-global-time/0_short.py
@@ -0,0 +1,4 @@
+# RUN: %{python} %s
+from __future__ import print_function
+
+print("short program")
Index: utils/lit/tests/Inputs/shtest-max-global-time/1_infinite_loop.py
===================================================================
--- /dev/null
+++ utils/lit/tests/Inputs/shtest-max-global-time/1_infinite_loop.py
@@ -0,0 +1,9 @@
+# RUN: %{python} %s
+from __future__ import print_function
+
+import sys
+
+print("Running infinite loop")
+sys.stdout.flush() # Make sure the print gets flushed so it appears in lit output.
+while True:
+    pass
Index: utils/lit/tests/Inputs/shtest-max-global-time/lit.cfg
===================================================================
--- /dev/null
+++ utils/lit/tests/Inputs/shtest-max-global-time/lit.cfg
@@ -0,0 +1,17 @@
+# -*- Python -*-
+import os
+import sys
+
+import lit.formats
+
+config.name = 'max_global_time'
+
+config.test_format = lit.formats.ShTest(execute_external=True)
+config.suffixes = ['.py']
+
+config.test_source_root = os.path.dirname(__file__)
+config.test_exec_root = config.test_source_root
+config.target_triple = '(unused)'
+src_root = os.path.join(config.test_source_root, '..')
+config.environment['PYTHONPATH'] = src_root
+config.substitutions.append(('%{python}', sys.executable))
Index: utils/lit/tests/shtest-max-global-time-multiprocess.py
===================================================================
--- /dev/null
+++ utils/lit/tests/shtest-max-global-time-multiprocess.py
@@ -0,0 +1,17 @@
+# RUN: not %{lit} \
+# RUN:   %{inputs}/shtest-max-global-time/0_short.py \
+# RUN:   %{inputs}/shtest-max-global-time/1_infinite_loop.py \
+# RUN: -j1 -v --max-time 5 > %t.out 2> %t.err
+# RUN: FileCheck --check-prefix=CHECK-OUT < %t.out %s
+# RUN: FileCheck --check-prefix=CHECK-ERR < %t.err %s
+
+# CHECK-OUT: PASS: max_global_time :: 0_short.py
+
+# FIXME: This test should really be a TIMEOUT because we started running
+# it and had to kill it.
+# CHECK-OUT: Unresolved Tests (1):
+# CHECK-OUT-NEXT: max_global_time :: 1_infinite_loop.py
+
+# CHECK-OUT:        Expected Passes    : 1
+# CHECK-OUT:        Unresolved Tests   : 1
+# CHECK-ERR: warning: Used up max time. Not running any more tests
Index: utils/lit/tests/shtest-max-global-time-single-process.py
===================================================================
--- /dev/null
+++ utils/lit/tests/shtest-max-global-time-single-process.py
@@ -0,0 +1,22 @@
+# FIXME: The current implementation of `--max-time` when using
+# a single process uses the per test timeout feature which
+# requires the psutil python module.
+
+# REQUIRES: python-psutil
+# PR33944
+# XFAIL: windows
+
+# RUN: not %{lit} \
+# RUN:   %{inputs}/shtest-max-global-time/0_short.py \
+# RUN:   %{inputs}/shtest-max-global-time/1_infinite_loop.py \
+# RUN: -j1 -v --max-time 5 --single-process > %t.out 2> %t.err
+# RUN: FileCheck --check-prefix=CHECK-OUT < %t.out %s
+# RUN: FileCheck --check-prefix=CHECK-ERR < %t.err %s
+
+# CHECK-OUT: PASS: max_global_time :: 0_short.py
+
+# CHECK-OUT: TIMEOUT: max_global_time :: 1_infinite_loop.py
+
+# CHECK-OUT: Expected Passes    : 1
+# CHECK-OUT: Individual Timeouts: 1
+# CHECK-ERR: warning: Used up max time. Not running any more tests