diff --git a/Lib/test/test_complex.py b/Lib/test/test_complex.py
@@ -1,6 +1,8 @@
+import errno
 import unittest
 import sys
 from test import support
+from test.support import import_helper
 from test.support.testcase import ComplexesAreIdenticalMixin
 from test.support.numbers import (
     VALID_UNDERSCORE_LITERALS,
@@ -9,6 +11,7 @@
 
 from random import random
 from math import isnan, copysign
+import cmath
 import operator
 
 INF = float("inf")
@@ -789,8 +792,30 @@ def test_abs(self):
         for num in nums:
             self.assertAlmostEqual((num.real**2 + num.imag**2)  ** 0.5, abs(num))
 
+        for x in 0.0, -0.0, INF, -INF, NAN:
+            for y in 0.0, -0.0, INF, -INF, NAN:
+                with self.subTest(x=x, y=y):
+                    z = complex(x, y)
+                    r = abs(z)
+                    if cmath.isfinite(z):
+                        self.assertFloatsAreIdentical(r, 0.0)
+                    elif cmath.isinf(z):
+                        self.assertEqual(r, INF)
+                    else:
+                        self.assertTrue(cmath.isnan(z))
+                        self.assertTrue(isnan(r))
+
         self.assertRaises(OverflowError, abs, complex(DBL_MAX, DBL_MAX))
 
+    def test_abs_errno_handling(self):
+        _testcapi = import_helper.import_module('_testcapi')
+        z = complex('nan')
+        _testcapi.set_errno(errno.ERANGE)
+        try:
+            self.assertTrue(isnan(abs(z)))
+        finally:
+            _testcapi.set_errno(0)
+
     def test_repr_str(self):
         def test(v, expected, test_fn=self.assertEqual):
             test_fn(repr(v), expected)

diff --git a/Misc/NEWS.d/next/Core_and_Builtins/2026-08-11-06-04-26.gh-issue-155526.W7ZHXu.rst b/Misc/NEWS.d/next/Core_and_Builtins/2026-08-11-06-04-26.gh-issue-155526.W7ZHXu.rst
@@ -0,0 +1,3 @@
+Fix spurious :exc:`OverflowError` for ``abs(nanj)`` in case :c:data:`errno` was
+previously set to :c:macro:`!ERANGE` by some library call.
+Patch by Sergey B Kirpichev.
diff --git a/Modules/cmathmodule.c b/Modules/cmathmodule.c
@@ -1029,8 +1029,8 @@ cmath_polar_impl(PyObject *module, Py_complex z)
 {
     double r, phi;
 
-    errno = 0;
     phi = atan2(z.imag, z.real); /* should not cause any exception */
+    errno = 0;
     r = _Py_c_abs(z); /* sets errno to ERANGE on overflow */
     if (errno != 0)
         return math_error();

diff --git a/Objects/complexobject.c b/Objects/complexobject.c
@@ -796,7 +796,10 @@ static PyObject *
 complex_abs(PyObject *op)
 {
     PyComplexObject *v = _PyComplexObject_CAST(op);
-    double result = _Py_c_abs(v->cval);
+    double result;
+
+    errno = 0;
+    result = _Py_c_abs(v->cval);
     if (errno == ERANGE) {
         PyErr_SetString(PyExc_OverflowError,
                         "absolute value too large");