In a phylogenetic systematics (a classification system that takes into account only derived - evolutionarily novel - characteristics)
http://en.wikipedia.org/wiki/Phylogenetic_nomenclature
(I must add a lot of citations to that article, among other things.)
Most researches agree that Reptilia is a group that include crocodiles, turtles, lizzards, snakes, tuataras their most recent common ancestor and all its descendants.
(Robert T Bakker once argued to elect a class to dinosaurs - including birds - but he was not using the phylogenetic way of thought.)