diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index f77f631a4..3fe35182f 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -1494,6 +1494,12 @@ bool Tokenizer::tokenize(std::istream &code, const char FileName[], const std::s
 
     // simplify function pointers
     simplifyFunctionPointers();
+
+    // "if (not p)" => "if (!p)"
+    // "if (p and q)" => "if (p && q)"
+    // "if (p or q)" => "if (p || q)"
+    while (simplifyLogicalOperators());
+
 //updateClassList();
     setVarId();
 
@@ -3238,7 +3244,6 @@ bool Tokenizer::simplifyTokenList()
         }
     }
 
-    simplifyLogicalOperators();
     simplifyCasts();
 
     // simplify "x=realloc(y,0);" => "free(y); x=0;"..
@@ -4895,32 +4900,43 @@ void Tokenizer::simplifyIfSameInnerCondition()
 }
 
 
-void Tokenizer::simplifyLogicalOperators()
+bool Tokenizer::simplifyLogicalOperators()
 {
+    bool ret = false;
+
     // "if (not p)" => "if (!p)"
-    // "if (p and q)" => "if (p and q)"
+    // "if (p and q)" => "if (p && q)"
+    // "if (p or q)" => "if (p || q)"
     for (Token *tok = _tokens; tok; tok = tok->next())
     {
         if (Token::Match(tok, "if|while ( not %var%"))
         {
             tok->tokAt(2)->str("!");
+            ret = true;
         }
         else if (Token::Match(tok, "&& not %var%"))
         {
             tok->next()->str("!");
+            ret = true;
         }
         else if (Token::Match(tok, "|| not %var%"))
         {
             tok->next()->str("!");
+            ret = true;
         }
         // "%var%|) and %var%|("
-        else if (tok->str() == "and" &&
+        else if (Token::Match(tok, "and|or") &&
                  ((Token::Match(tok->previous(), "%var%") || tok->previous()->str() == ")") ||
                   (Token::Match(tok->next(), "%var%") || tok->next()->str() == "(")))
         {
-            tok->str("&&");
+            if (tok->str() == "and")
+                tok->str("&&");
+            else
+                tok->str("||");
+            ret = true;
         }
     }
+    return ret;
 }
 
 // int i(0); => int i; i = 0;
diff --git a/lib/tokenize.h b/lib/tokenize.h
index 0de654c5a..d9855dedf 100644
--- a/lib/tokenize.h
+++ b/lib/tokenize.h
@@ -215,7 +215,7 @@ public:
      * - "if (not p)" => "if (!p)"
      * - "if (p and q)" => "if (p && q)"
      */
-    void simplifyLogicalOperators();
+    bool simplifyLogicalOperators();
 
     /**
      * Simplify comma into a semicolon when possible:
diff --git a/test/testsimplifytokens.cpp b/test/testsimplifytokens.cpp
index 75a77dfd5..b26a7ab9f 100644
--- a/test/testsimplifytokens.cpp
+++ b/test/testsimplifytokens.cpp
@@ -118,6 +118,9 @@ private:
         // Simplify "and" to "&&" (#620)
         TEST_CASE(and1);
 
+        // Simplify "or" to "||"
+        TEST_CASE(or1);
+
         TEST_CASE(comma_keyword);
         TEST_CASE(remove_comma);
 
@@ -1978,8 +1981,6 @@ private:
         std::istringstream istr(code);
         tokenizer.tokenize(istr, "test.cpp");
 
-        tokenizer.simplifyLogicalOperators();
-
         std::ostringstream ostr;
         for (const Token *tok1 = tokenizer.tokens(); tok1; tok1 = tok1->next())
             ostr << (tok1->previous() ? " " : "") << tok1->str();
@@ -2007,6 +2008,27 @@ private:
 
         ASSERT_EQUALS("if ( p && bar ( ) ) { ; }",
                       simplifyLogicalOperators("if (p and bar()) ;"));
+
+        ASSERT_EQUALS("if ( p && ! q )",
+                      simplifyLogicalOperators("if (p and not q)"));
+    }
+
+    void or1()
+    {
+        ASSERT_EQUALS("if ( p || q ) { ; }",
+                      simplifyLogicalOperators("if (p or q) ;"));
+
+        ASSERT_EQUALS("if ( foo ( ) || q ) { ; }",
+                      simplifyLogicalOperators("if (foo() or q) ;"));
+
+        ASSERT_EQUALS("if ( foo ( ) || bar ( ) ) { ; }",
+                      simplifyLogicalOperators("if (foo() or bar()) ;"));
+
+        ASSERT_EQUALS("if ( p || bar ( ) ) { ; }",
+                      simplifyLogicalOperators("if (p or bar()) ;"));
+
+        ASSERT_EQUALS("if ( p || ! q )",
+                      simplifyLogicalOperators("if (p or not q)"));
     }
 
     void comma_keyword()