I noticed these kind of constructors in the classes:

function NexmoMessage ($api_key, $api_secret) {
    $this->nx_key = $api_key;
    $this->nx_secret = $api_secret;
}

I believe these are PHP4 style constructors and if I'm not mistaken, will be deprecated. It might be good to replace them with proper constructors instead:

http://php.net/manual/en/language.oop5.decon.php