Abstract : This work is concerned with the application of the second-order nonlinear homogenization procedure of Ponte Casta~neda (2002) to generate estimates for the e®ective behavior of viscoplastic porous materials. The main concept behind this procedure is the construction of suitable variational principles utilizing the idea of a \linear comparison composite" to generate corresponding estimates for the nonlinear porous media. Thus, the main objective of this work is to propose a general constitutive model that accounts for the evolution of the microstructure and hence the induced anisotropy resulting when the porous material is subjected to ¯nite deformations. The model is constructed in such a way that it reproduces exactly the behavior of a \composite-sphere assemblage" in the limit of hydrostatic loadings, and therefore coincides with the hydrostatic limit of Gurson's (1977) criterion in the special case of ideal plasticity and isotropic microstructures. As a consequence, the new model improves on earlier homogenization estimates, which have been found to be quite accurate for low triaxialities but overly sti® for su±ciently high triaxialities and nonlinearities. Additionally, the estimates delivered by the model exhibit a dependence on the third invariant of the macroscopic stress tensor, which has a signi¯cant e®ect on the e®ective response of the material at moderate and high stress triaxialities. Finally, the above-mentioned results are generalized to more complex anisotropic microstructures (ar- bitrary pore shapes and orientation) and general, three-dimensional loadings, leading to overall anisotropic response for the porous material. The model is then extended to account for the evolution of microstructure when the material is subjected to ¯nite deformations. To validate the proposed model, ¯nite element axisym- metric unit-cell calculations are performed and the agreement is found to be very good for the entire range of stress triaxialities and nonlinearities considered.