The problem of homology versus analogy of different craniological character states shared by Anguimorpha and Scincomorpha is analyzed. Only two character states, if any, may be tentatively considered as synapomorphies in both taxa. These are: low, tubular skull shape and broad, flat frontals. Other craniological features displaying similar states In both infra orders are regarded as parallel structures. Morphoclinal sequences of states of different craniological characters are proposed. The derived pattern of tooth replacement is regarded as the earliest and the most important achievement of the anguimorphan lizards which is probably the only autapomorphy of this infra order. A certain pattern of the brain case is regarded as synapomorphlc in the Platynota and Diploglossa, the two superfamllles that probably do not cover the range of the infra order.

Key words: Sauria, craniology, cladistics.