The interaction of a fast stellar wind with an outer slower wind gives rise to two layers of shocked gas separated by a contact discontinuity. The structure of the interaction region is self-similar if each wind is characterized by a constant mass loss rate, wind velocity, and gas sound speed. The self-similar structure is illustrated for a variety of wind parameters on the assumption that the flow is either adiabatic with gamma = 5/3 or isothermal. The results are in good agreement with numerical hydrodynamic calculations of interplanetary shock waves. The structure of the inner shocked layer is important for the colliding wind theory of planetary nebulae. It is also noted that the theory may be applicable to some of the ring nebulae observed around Wolf-Rayet stars.