diff --git a/Lib/test/test_bigaddrspace.py b/Lib/test/test_bigaddrspace.py
new file mode 100644
index 000000000..50272e996
--- /dev/null
+++ b/Lib/test/test_bigaddrspace.py
@@ -0,0 +1,98 @@
+"""
+These tests are meant to exercise that requests to create objects bigger
+than what the address space allows are properly met with an OverflowError
+(rather than crash weirdly).
+
+Primarily, this means 32-bit builds with at least 2 GiB of available memory.
+You need to pass the -M option to regrtest (e.g. "-M 2.1G") for tests to
+be enabled.
+"""
+
+from test import support
+from test.support import bigaddrspacetest, MAX_Py_ssize_t
+
+import unittest
+import operator
+import sys
+
+
+class BytesTest(unittest.TestCase):
+
+    @bigaddrspacetest
+    def test_concat(self):
+        # Allocate a bytestring that's near the maximum size allowed by
+        # the address space, and then try to build a new, larger one through
+        # concatenation.
+        try:
+            x = b"x" * (MAX_Py_ssize_t - 128)
+            self.assertRaises(OverflowError, operator.add, x, b"x" * 128)
+        finally:
+            x = None
+
+    @bigaddrspacetest
+    def test_optimized_concat(self):
+        try:
+            x = b"x" * (MAX_Py_ssize_t - 128)
+
+            with self.assertRaises(OverflowError) as cm:
+                # this statement used a fast path in ceval.c
+                x = x + b"x" * 128
+
+            with self.assertRaises(OverflowError) as cm:
+                # this statement used a fast path in ceval.c
+                x +=  b"x" * 128
+        finally:
+            x = None
+
+    @bigaddrspacetest
+    def test_repeat(self):
+        try:
+            x = b"x" * (MAX_Py_ssize_t - 128)
+            self.assertRaises(OverflowError, operator.mul, x, 128)
+        finally:
+            x = None
+
+
+class StrTest(unittest.TestCase):
+
+    unicodesize = 4
+
+    @bigaddrspacetest
+    def test_concat(self):
+        try:
+            # Create a string that would fill almost the address space
+            x = "x" * int(MAX_Py_ssize_t // (1.1 * self.unicodesize))
+            # Unicode objects trigger MemoryError in case an operation that's
+            # going to cause a size overflow is executed
+            self.assertRaises(MemoryError, operator.add, x, x)
+        finally:
+            x = None
+
+    @bigaddrspacetest
+    def test_optimized_concat(self):
+        try:
+            x = "x" * int(MAX_Py_ssize_t // (1.1 * self.unicodesize))
+
+            with self.assertRaises(MemoryError) as cm:
+                # this statement uses a fast path in ceval.c
+                x = x + x
+
+            with self.assertRaises(MemoryError) as cm:
+                # this statement uses a fast path in ceval.c
+                x +=  x
+        finally:
+            x = None
+
+    @bigaddrspacetest
+    def test_repeat(self):
+        try:
+            x = "x" * int(MAX_Py_ssize_t // (1.1 * self.unicodesize))
+            self.assertRaises(MemoryError, operator.mul, x, 2)
+        finally:
+            x = None
+
+
+if __name__ == '__main__':
+    if len(sys.argv) > 1:
+        support.set_memlimit(sys.argv[1])
+    unittest.main()