We analyze the steady state situation in which two separate and counterstreaming plasmas (assumed to be incompressible) carrying antiparallel magnetic fields are separated by a resistive current layer. Exact solutions are presented which describe the stagnation point flow pattern and magnetic field behavior which result. They incorporate the effects of viscosity, which enables us to model flows with vorticity. The uniform plasma flow which is obtained at large distances from the current layer allows is to specify finite values of the asymptotic magnetic field. Our exact solutions complement those of a different type obtained by B. U. ¿. Sonnerup and E. R. Priest (1975) which assume potential flow, i.e., zero vorticity. The results we obtain are discussed in relation to observational features at the Earth's magnetopause. ¿ American Geophysical Union 1988