Slow, stable, rectilinear crack propagation is investigated for porous, elastoplastic solids displaying combined isotropic and kinematic hardening. The Gurson model with constant porosity, and therefore the associated flow rule, is used as the constitutive description. An asymptotic analysis of crack-tip fields is performed under Mode I, steady-state, small-strain, plane stress and plane strain conditions. A continuous distribution of asymptotic near-tip fields is found. However, the possibility of the appearance of stress jumps in the asymptotic fields is analysed in detail. The results show many interesting features, which are related to the presence of both porosity and Bauschinger effect.