diff --git a/lib/checkclass.cpp b/lib/checkclass.cpp
index 6fd15dafc72..3c461c0ab44 100644
--- a/lib/checkclass.cpp
+++ b/lib/checkclass.cpp
@@ -319,6 +319,11 @@ void CheckClass::constructors()
     }
 }
 
+static bool isPermissibleConversion(const std::string& type)
+{
+    return type == "std::initializer_list" || type == "std::nullptr_t";
+}
+
 void CheckClass::checkExplicitConstructors()
 {
     if (!mSettings->severity.isEnabled(Severity::style) && !mSettings->isPremiumEnabled("noExplicitConstructor"))
@@ -357,7 +362,7 @@ void CheckClass::checkExplicitConstructors()
                 func.type != FunctionType::eCopyConstructor &&
                 func.type != FunctionType::eMoveConstructor &&
                 !(func.templateDef && Token::simpleMatch(func.argumentList.front().typeEndToken(), "...")) &&
-                func.argumentList.front().getTypeName() != "std::initializer_list") {
+                !isPermissibleConversion(func.argumentList.front().getTypeName())) {
                 noExplicitConstructorError(func.tokenDef, scope->className, scope->type == ScopeType::eStruct);
             }
         }
diff --git a/test/testclass.cpp b/test/testclass.cpp
index 8eeb7eb7696..2f37c579816 100644
--- a/test/testclass.cpp
+++ b/test/testclass.cpp
@@ -503,6 +503,14 @@ class TestClass : public TestFixture {
         ASSERT_EQUALS("[test.cpp:3:5]: (style) Class 'Color' has a constructor with 1 argument that is not explicit. [noExplicitConstructor]\n"
                       "[test.cpp:4:5]: (style) Class 'Color' has a constructor with 1 argument that is not explicit. [noExplicitConstructor]\n",
                       errout_str());
+
+        checkExplicitConstructors("template <typename T>\n" // #13878
+                                  "struct S {\n"
+                                  "    S(std::nullptr_t) {}\n"
+                                  "    explicit S(T* p) : m(p) {}\n"
+                                  "    T* m{};\n"
+                                  "};\n");
+        ASSERT_EQUALS("", errout_str());
     }
 
 #define checkDuplInheritedMembers(...) checkDuplInheritedMembers_( __FILE__, __LINE__, __VA_ARGS__)