The structure and the critical resolved shear stress for the motion of the straight a/2[110] edge and screw dislocations in Fe-Ni-Cr and Fe-Ni-Cr-N austenite have been analysed using the conjugate gradient method to minimize the potential energy of the crystal and the embedded atom method to quantify atomic interactions at 0 K. In Fe-Ni-Cr austenite both the edge and the screw dislocations dissociate along one of the {111} planes forming a stacking-fault ribbon. The ribbon widths are comparable to their values calculated using continuum theory. Dissociated edge and screw dislocations require very similar levels of shear stress for their motion. In Fe-Ni-Cr-N austenite, the structure of the dislocation core of the a/2[110] edge dislocation does not seem to be significantly affected by the presence of nitrogen. In sharp contrast, the core structure of the dissociated a/2[110] dislocation undergoes a major change, resulting in spreading of the core on to two or more non-parallel planes. As a result, a significantly higher level of stress is required for the motion of a screw than an edge dislocation. Under certain conditions the interaction of nitrogen atoms with screw dislocations can result in pinning of the dislocations. The potential mechanism for the motion of the pinned screw dislocations by formation and motion of edge-type kinks is briefly discussed.