You can use below regular expression to extract desired string.
<errorcode>.*<\/message>
string str = @"<processresponse xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns:xsd='http://www.w3.org/2001/XMLSchema'><extensiondata /><errorcode>0</errorcode><errormessage /><message>successful.</message></processresponse>";
Regex reg = new Regex(@"<errorcode>.*<\/message>");
Match tmp = reg.Match(str);
Console.WriteLine(tmp.Value);