diff --git a/Lib/compileall.py b/Lib/compileall.py
index 1831ad749f2b17..966bc4b2b55ea4 100644
--- a/Lib/compileall.py
+++ b/Lib/compileall.py
@@ -206,8 +206,8 @@ def compile_file(fullname, ddir=None, force=False, rx=None, quiet=0,
             if not force:
                 try:
                     mtime = int(os.stat(fullname).st_mtime)
-                    expect = struct.pack('<4sll', importlib.util.MAGIC_NUMBER,
-                                         0, mtime)
+                    expect = struct.pack('<4sLL', importlib.util.MAGIC_NUMBER,
+                                         0, mtime & 0xFFFF_FFFF)
                     for cfile in opt_cfiles.values():
                         with open(cfile, 'rb') as chandle:
                             actual = chandle.read(12)
diff --git a/Lib/test/test_compileall.py b/Lib/test/test_compileall.py
index cb59fd71b38254..7ca056fd0922af 100644
--- a/Lib/test/test_compileall.py
+++ b/Lib/test/test_compileall.py
@@ -55,9 +55,28 @@ def timestamp_metadata(self):
         with open(self.bc_path, 'rb') as file:
             data = file.read(12)
         mtime = int(os.stat(self.source_path).st_mtime)
-        compare = struct.pack('<4sll', importlib.util.MAGIC_NUMBER, 0, mtime)
+        compare = struct.pack('<4sLL', importlib.util.MAGIC_NUMBER, 0,
+                              mtime & 0xFFFF_FFFF)
         return data, compare
 
+    def test_year_2038_mtime_compilation(self):
+        # Test to make sure we can handle mtimes larger than what a 32-bit
+        # signed number can hold as part of bpo-34990
+        try:
+            os.utime(self.source_path, (2**32 - 1, 2**32 - 1))
+        except (OverflowError, OSError):
+            self.skipTest("filesystem doesn't support timestamps near 2**32")
+        self.assertTrue(compileall.compile_file(self.source_path))
+
+    def test_larger_than_32_bit_times(self):
+        # This is similar to the test above but we skip it if the OS doesn't
+        # support modification times larger than 32-bits.
+        try:
+            os.utime(self.source_path, (2**35, 2**35))
+        except (OverflowError, OSError):
+            self.skipTest("filesystem doesn't support large timestamps")
+        self.assertTrue(compileall.compile_file(self.source_path))
+
     def recreation_check(self, metadata):
         """Check that compileall recreates bytecode when the new metadata is
         used."""
@@ -76,7 +95,7 @@ def recreation_check(self, metadata):
 
     def test_mtime(self):
         # Test a change in mtime leads to a new .pyc.
-        self.recreation_check(struct.pack('<4sll', importlib.util.MAGIC_NUMBER,
+        self.recreation_check(struct.pack('<4sLL', importlib.util.MAGIC_NUMBER,
                                           0, 1))
 
     def test_magic_number(self):
diff --git a/Lib/test/test_zipimport.py b/Lib/test/test_zipimport.py
index 2af8689c1d2cb2..a08c96698ab791 100644
--- a/Lib/test/test_zipimport.py
+++ b/Lib/test/test_zipimport.py
@@ -34,14 +34,9 @@ def get_file():
 
 def make_pyc(co, mtime, size):
     data = marshal.dumps(co)
-    if type(mtime) is type(0.0):
-        # Mac mtimes need a bit of special casing
-        if mtime < 0x7fffffff:
-            mtime = int(mtime)
-        else:
-            mtime = int(-0x100000000 + int(mtime))
     pyc = (importlib.util.MAGIC_NUMBER +
-        struct.pack("<iii", 0, int(mtime), size & 0xFFFFFFFF) + data)
+        struct.pack("<iLL", 0,
+                    int(mtime) & 0xFFFF_FFFF, size & 0xFFFF_FFFF) + data)
     return pyc
 
 def module_path_to_dotted_name(path):
@@ -253,6 +248,14 @@ def testBadMTime(self):
                  TESTMOD + pyc_ext: (NOW, badtime_pyc)}
         self.doTest(".py", files, TESTMOD)
 
+    def test2038MTime(self):
+        # Make sure we can handle mtimes larger than what a 32-bit signed number
+        # can hold.
+        twenty_thirty_eight_pyc = make_pyc(test_co, 2**32 - 1, len(test_src))
+        files = {TESTMOD + ".py": (NOW, test_src),
+                 TESTMOD + pyc_ext: (NOW, twenty_thirty_eight_pyc)}
+        self.doTest(".py", files, TESTMOD)
+
     def testPackage(self):
         packdir = TESTPACK + os.sep
         files = {packdir + "__init__" + pyc_ext: (NOW, test_pyc),
diff --git a/Misc/NEWS.d/next/Library/2020-04-24-20-39-38.bpo-34990.3SmL9M.rst b/Misc/NEWS.d/next/Library/2020-04-24-20-39-38.bpo-34990.3SmL9M.rst
new file mode 100644
index 00000000000000..d420b5dce1e3b5
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-04-24-20-39-38.bpo-34990.3SmL9M.rst
@@ -0,0 +1,2 @@
+Fixed a Y2k38 bug in the compileall module where it would fail to compile
+files with a modification time after the year 2038.