diff --git a/CHANGELOG.md b/CHANGELOG.md
index 7e414182..3f263997 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -3,6 +3,10 @@ Changelog
 
 ## 2.1.0
 
+### Added
+
+- Added `notList` to check if an array is associative, with string _or_ integer keys.
+
 ### Fixed
 
 - Corrected `@param` declaration for `isMap`.
diff --git a/README.md b/README.md
index 7c10111b..c7535b2b 100644
--- a/README.md
+++ b/README.md
@@ -207,6 +207,7 @@ Method                                             | Description
 `countBetween($array, $min, $max, $message = '')`  | Check that an array has a count in the given range
 `isList($array, $message = '')`                    | Check that an array is a non-associative list
 `isNonEmptyList($array, $message = '')`            | Check that an array is a non-associative list, and not empty
+`notList($array, $message = '')`                   | Check that an array is associative
 `isMap($array, $message = '')`                     | Check that an array is associative and has strings as keys
 `isNonEmptyMap($array, $message = '')`             | Check that an array is associative and has strings as keys, and is not empty
 
diff --git a/src/Assert.php b/src/Assert.php
index 20116cc1..59723417 100644
--- a/src/Assert.php
+++ b/src/Assert.php
@@ -1984,9 +1984,13 @@ public static function countBetween(mixed $array, mixed $min, mixed $max, string
     /**
      * @psalm-pure
      *
-     * @psalm-assert list $array
+     * @template T
+     *
+     * @psalm-assert list<T> $array
+     *
+     * @param mixed|array<array-key, T> $array
      *
-     * @psalm-return list
+     * @return list<T>
      *
      * @throws InvalidArgumentException
      */
@@ -2018,6 +2022,32 @@ public static function isNonEmptyList(mixed $array, string $message = ''): array
         return $array;
     }
 
+    /**
+     * @psalm-pure
+     *
+     * @template T
+     *
+     * @psalm-assert array<array-key, T> $array
+     *
+     * @param mixed|array<array-key, T> $array
+     *
+     * @return array<array-key, T>
+     *
+     * @throws InvalidArgumentException
+     */
+    public static function notList(mixed $array, string $message = ''): array
+    {
+        static::isArray($array, $message);
+
+        if (\array_is_list($array)) {
+            static::reportInvalidArgument(
+                $message ?: 'Expected non-list - associative array.'
+            );
+        }
+
+        return $array;
+    }
+
     /**
      * @psalm-pure
      *
@@ -2034,6 +2064,7 @@ public static function isNonEmptyList(mixed $array, string $message = ''): array
     public static function isMap(mixed $array, string $message = ''): array
     {
         static::isArray($array, $message);
+        static::allString(array_keys($array), $message);
 
         if (\count($array) > 0 && \array_is_list($array)) {
             static::reportInvalidArgument(
diff --git a/src/Mixin.php b/src/Mixin.php
index ad0aeec8..464248a8 100644
--- a/src/Mixin.php
+++ b/src/Mixin.php
@@ -4781,9 +4781,12 @@ public static function allNullOrCountBetween(mixed $array, mixed $min, mixed $ma
     /**
      * @psalm-pure
      *
-     * @psalm-assert list|null $array
+     * @template T
+     * @psalm-assert list<T>|null $array
+     *
+     * @param mixed|array<array-key, T>|null $array
      *
-     * @return list|null
+     * @return list<T>|null
      *
      * @throws InvalidArgumentException
      */
@@ -4797,9 +4800,12 @@ public static function nullOrIsList(mixed $array, string $message = ''): mixed
     /**
      * @psalm-pure
      *
-     * @psalm-assert iterable<list> $array
+     * @template T
+     * @psalm-assert iterable<list<T>> $array
+     *
+     * @param iterable<mixed|array<array-key, T>> $array
      *
-     * @return iterable<list>
+     * @return iterable<list<T>>
      *
      * @throws InvalidArgumentException
      */
@@ -4817,9 +4823,12 @@ public static function allIsList(mixed $array, string $message = ''): mixed
     /**
      * @psalm-pure
      *
-     * @psalm-assert iterable<list|null> $array
+     * @template T
+     * @psalm-assert iterable<list<T>|null> $array
+     *
+     * @param iterable<mixed|array<array-key, T>|null> $array
      *
-     * @return iterable<list|null>
+     * @return iterable<list<T>|null>
      *
      * @throws InvalidArgumentException
      */
@@ -4890,6 +4899,71 @@ public static function allNullOrIsNonEmptyList(mixed $array, string $message = '
         return $array;
     }
 
+    /**
+     * @psalm-pure
+     *
+     * @template T
+     * @psalm-assert array<array-key, T>|null $array
+     *
+     * @param mixed|array<array-key, T>|null $array
+     *
+     * @return array<array-key, T>|null
+     *
+     * @throws InvalidArgumentException
+     */
+    public static function nullOrNotList(mixed $array, string $message = ''): mixed
+    {
+        null === $array || static::notList($array, $message);
+
+        return $array;
+    }
+
+    /**
+     * @psalm-pure
+     *
+     * @template T
+     * @psalm-assert iterable<array<array-key, T>> $array
+     *
+     * @param iterable<mixed|array<array-key, T>> $array
+     *
+     * @return iterable<array<array-key, T>>
+     *
+     * @throws InvalidArgumentException
+     */
+    public static function allNotList(mixed $array, string $message = ''): mixed
+    {
+        static::isIterable($array);
+
+        foreach ($array as $entry) {
+            static::notList($entry, $message);
+        }
+
+        return $array;
+    }
+
+    /**
+     * @psalm-pure
+     *
+     * @template T
+     * @psalm-assert iterable<array<array-key, T>|null> $array
+     *
+     * @param iterable<mixed|array<array-key, T>|null> $array
+     *
+     * @return iterable<array<array-key, T>|null>
+     *
+     * @throws InvalidArgumentException
+     */
+    public static function allNullOrNotList(mixed $array, string $message = ''): mixed
+    {
+        static::isIterable($array);
+
+        foreach ($array as $entry) {
+            null === $entry || static::notList($entry, $message);
+        }
+
+        return $array;
+    }
+
     /**
      * @psalm-pure
      *
diff --git a/tests/AssertTest.php b/tests/AssertTest.php
index 7ec8c6fe..1339fccb 100644
--- a/tests/AssertTest.php
+++ b/tests/AssertTest.php
@@ -536,6 +536,10 @@ public static function getTests(): array
             ['isList', [[['foo' => 'bar'], ['baz' => 'tab']]], true],
             ['isList', [$nanList], true],
             ['isList', [$normalList], true],
+            ['notList', [[]], false],
+            ['notList', [[0 => 1, 2 => 3]], true],
+            ['notList', [['key' => 1, 'foo' => 2]], true],
+            ['notList', [[1, 2, 3]], false],
             ['isNonEmptyList', [[1, 2, 3]], true],
             ['isNonEmptyList', [[]], false],
             ['isNonEmptyList', [[0 => 1, 2 => 3]], false],
@@ -546,12 +550,12 @@ public static function getTests(): array
             ['isNonEmptyList', [[false]], true],
             ['isNonEmptyList', [[[1], [2]]], true],
             ['isNonEmptyList', [[['foo' => 'bar'], ['baz' => 'tab']]], true],
-            ['isMap', [['key' => 1, 'foo' => 2]], true],
-            ['isMap', [[0 => 1, 2 => 3]], true],
             ['isMap', [[]], true],
+            ['isMap', [['key' => 1, 'foo' => 2]], true],
+            ['isMap', [[0 => 1, 2 => 3]], false],
             ['isMap', [[1, 2, 3]], false],
             ['isNonEmptyMap', [['key' => 1, 'foo' => 2]], true],
-            ['isNonEmptyMap', [[0 => 1, 2 => 3]], true],
+            ['isNonEmptyMap', [[0 => 1, 2 => 3]], false],
             ['isNonEmptyMap', [[]], false],
             ['isNonEmptyMap', [[1, 2, 3]], false],
             ['uuid', ['00000000-0000-0000-0000-000000000000'], true],
diff --git a/tests/static-analysis/assert-notList.php b/tests/static-analysis/assert-notList.php
new file mode 100644
index 00000000..d9019eb1
--- /dev/null
+++ b/tests/static-analysis/assert-notList.php
@@ -0,0 +1,72 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Webmozart\Assert\Tests\StaticAnalysis;
+
+use stdClass;
+use Webmozart\Assert\Assert;
+
+/**
+ * @psalm-pure
+ *
+ * @param mixed $value
+ *
+ * @return array<array-key, mixed>
+ */
+function notList(mixed $value): array
+{
+    Assert::notList($value);
+
+    return $value;
+}
+
+/**
+ * @psalm-pure
+ *
+ * @param array<array-key, stdClass> $value
+ *
+ * @return array<array-key, stdClass>
+ */
+function isNotListWithKnownType(array $value): array
+{
+    Assert::notList($value);
+
+    return $value;
+}
+
+/**
+ * @psalm-pure
+ *
+ * @return null|array<array-key, mixed>
+ */
+function nullOrIsNotList(mixed $value): ?array
+{
+    Assert::nullOrNotList($value);
+
+    return $value;
+}
+
+/**
+ * @psalm-pure
+ *
+ * @return iterable<array-key, array<array-key, mixed>>
+ */
+function allNotList(mixed $value): iterable
+{
+    Assert::allNotList($value);
+
+    return $value;
+}
+
+/**
+ * @psalm-pure
+ *
+ * @return iterable<array-key, null|array<array-key, mixed>>
+ */
+function allNullOrNotList(mixed $value): iterable
+{
+    Assert::allNullOrNotList($value);
+
+    return $value;
+}