A two-and-a-half-dimensional two-ion fluid model (with gyrotropic pressure tensor) for the interaction of cometary pickup plasma with the solar wind has been developed. Whereas previous models have, in general, assumed a one-fluid plasma, this generalized model follows the evolution of two fluids: solar wind protons and cometary ions. The two fluids are coupled by the magnetic field and by coupling terms which are the velocity moments of the time relaxation model of Bhatnagar et al. [1954>. Furthermore, a gyrotropic pressure tensor replaces the isotropic pressure assumed in other models. Isotropization terms couple the pressures in the directions perpendicular and parallel to the magnetic field. Among the results received, the standoff distance of the shock increased significantly when the isotropization rate was reduced. The large cometary plasma pressure forces at the shock accelerated the cometary plasma along the shock. As a result, the cometary plasma drifted ahead of the solar wind along the shock flanks parallel to the magnetic field. Close to the nucleus of the comet in the far tail lobes and in the far inner tail the cometary plasma lagged behind the solar wind. ¿ 1998 American Geophysical Union