In the field of axiomatic, linear-elastic, two dimensional modeling of multilayered structures this paper addresses theories in view of the C z 0 requirements, i.e. both the zig-zag form of the displacement components along the thickness coordinate and the interlaminar equilibria at the interfaces for the transverse stress components are taken into account. First, existing single-layer models are reviewed: (1) it is remarked that they are of limited value to analyze problems in which an accurate description of the transverse normal stress and related consequences is requested; (2) it is concluded that such description would require the use of layer-wise theories. Moreover, it is single out that available layer-wise models do not fulfill a priori interlaminar equilibria. The contents of a recent author's work (Carrera 1994a, in press) have been extended to propose some layer-wise models as tools to fulfill a priori and complete the C z 0 requirements. Approximate solution procedures are referred and the governing equations have been presented in the form of a linear system of algebraic equations. The mixed and displacement formulations are described by employing a Reissner mixed variational theorem and by writing a weak form of the Hooke law, respectively.