diff --git a/include/xsimd/arch/xsimd_avx.hpp b/include/xsimd/arch/xsimd_avx.hpp
index 20bbf600f..9d93be071 100644
--- a/include/xsimd/arch/xsimd_avx.hpp
+++ b/include/xsimd/arch/xsimd_avx.hpp
@@ -925,12 +925,12 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<float, A> max(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx>) noexcept
         {
-            return _mm256_max_ps(self, other);
+            return _mm256_max_ps(other, self);
         }
         template <class A>
         XSIMD_INLINE batch<double, A> max(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx>) noexcept
         {
-            return _mm256_max_pd(self, other);
+            return _mm256_max_pd(other, self);
         }
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE batch<T, A> max(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx>) noexcept
@@ -942,12 +942,12 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<float, A> min(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx>) noexcept
         {
-            return _mm256_min_ps(self, other);
+            return _mm256_min_ps(other, self);
         }
         template <class A>
         XSIMD_INLINE batch<double, A> min(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx>) noexcept
         {
-            return _mm256_min_pd(self, other);
+            return _mm256_min_pd(other, self);
         }
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE batch<T, A> min(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx>) noexcept
diff --git a/include/xsimd/arch/xsimd_avx512f.hpp b/include/xsimd/arch/xsimd_avx512f.hpp
index 7073d9d4f..7d980a538 100644
--- a/include/xsimd/arch/xsimd_avx512f.hpp
+++ b/include/xsimd/arch/xsimd_avx512f.hpp
@@ -1326,12 +1326,12 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<float, A> max(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
         {
-            return _mm512_max_ps(self, other);
+            return _mm512_max_ps(other, self);
         }
         template <class A>
         XSIMD_INLINE batch<double, A> max(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
         {
-            return _mm512_max_pd(self, other);
+            return _mm512_max_pd(other, self);
         }
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE batch<T, A> max(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
@@ -1376,12 +1376,12 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<float, A> min(batch<float, A> const& self, batch<float, A> const& other, requires_arch<avx512f>) noexcept
         {
-            return _mm512_min_ps(self, other);
+            return _mm512_min_ps(other, self);
         }
         template <class A>
         XSIMD_INLINE batch<double, A> min(batch<double, A> const& self, batch<double, A> const& other, requires_arch<avx512f>) noexcept
         {
-            return _mm512_min_pd(self, other);
+            return _mm512_min_pd(other, self);
         }
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE batch<T, A> min(batch<T, A> const& self, batch<T, A> const& other, requires_arch<avx512f>) noexcept
diff --git a/include/xsimd/arch/xsimd_sse2.hpp b/include/xsimd/arch/xsimd_sse2.hpp
index e8ad82875..2e892de3a 100644
--- a/include/xsimd/arch/xsimd_sse2.hpp
+++ b/include/xsimd/arch/xsimd_sse2.hpp
@@ -1137,7 +1137,7 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<float, A> max(batch<float, A> const& self, batch<float, A> const& other, requires_arch<sse2>) noexcept
         {
-            return _mm_max_ps(self, other);
+            return _mm_max_ps(other, self);
         }
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE batch<T, A> max(batch<T, A> const& self, batch<T, A> const& other, requires_arch<sse2>) noexcept
@@ -1147,14 +1147,14 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<double, A> max(batch<double, A> const& self, batch<double, A> const& other, requires_arch<sse2>) noexcept
         {
-            return _mm_max_pd(self, other);
+            return _mm_max_pd(other, self);
         }
 
         // min
         template <class A>
         XSIMD_INLINE batch<float, A> min(batch<float, A> const& self, batch<float, A> const& other, requires_arch<sse2>) noexcept
         {
-            return _mm_min_ps(self, other);
+            return _mm_min_ps(other, self);
         }
         template <class A, class T, class = typename std::enable_if<std::is_integral<T>::value, void>::type>
         XSIMD_INLINE batch<T, A> min(batch<T, A> const& self, batch<T, A> const& other, requires_arch<sse2>) noexcept
@@ -1164,7 +1164,7 @@ namespace xsimd
         template <class A>
         XSIMD_INLINE batch<double, A> min(batch<double, A> const& self, batch<double, A> const& other, requires_arch<sse2>) noexcept
         {
-            return _mm_min_pd(self, other);
+            return _mm_min_pd(other, self);
         }
 
         // mul
diff --git a/test/test_xsimd_api.cpp b/test/test_xsimd_api.cpp
index bea9f1b86..26b7618ad 100644
--- a/test/test_xsimd_api.cpp
+++ b/test/test_xsimd_api.cpp
@@ -658,6 +658,29 @@ struct xsimd_api_float_types_functions
         value_type val(0);
         CHECK_EQ(extract(xsimd::log1p(T(val))), std::log1p(val));
     }
+
+    void test_max_nan()
+    {
+        value_type val0(2.7818);
+        value_type valN(NAN);
+#if XSIMD_WITH_AVX || XSIMD_WITH_SSE2
+        using isnan = doctest::IsNaN<value_type>;
+        CHECK_EQ(isnan(extract(xsimd::max(T(val0), T(valN)))), isnan(std::max(val0, valN)));
+        CHECK_EQ(isnan(extract(xsimd::max(T(valN), T(val0)))), isnan(std::max(valN, val0)));
+#endif
+    }
+
+    void test_min_nan()
+    {
+        value_type val0(2.7818);
+        value_type valN(NAN);
+#if XSIMD_WITH_AVX || XSIMD_WITH_SSE2
+        using isnan = doctest::IsNaN<value_type>;
+        CHECK_EQ(isnan(extract(xsimd::min(T(val0), T(valN)))), isnan(std::min(val0, valN)));
+        CHECK_EQ(isnan(extract(xsimd::min(T(valN), T(val0)))), isnan(std::min(valN, val0)));
+#endif
+    }
+
     void test_nearbyint()
     {
         value_type val(3.1);
@@ -929,6 +952,16 @@ TEST_CASE_TEMPLATE("[xsimd api | float types functions]", B, FLOAT_TYPES)
         Test.test_log1p();
     }
 
+    SUBCASE("max_nan")
+    {
+        Test.test_max_nan();
+    }
+
+    SUBCASE("min_nan")
+    {
+        Test.test_min_nan();
+    }
+
     SUBCASE("nearbyint")
     {
         Test.test_nearbyint();