Numerical solutions of a magnetohydrodynamic model are carried out to describe the nonlinear interaction of corotating high-speed streams near the solar equatorial plane. Two problems are studied. The first problem is to simulate the evolution of an idealized high-speed stream. Numerical solutions are obtained to represent the variations of flow velocity, magnetic field, plasma density, temperature, and conduction heat flux in the interaction region. They demonstrate that the dynamical itneraction and heat conduction process are responsible for the thermal structure of a high-speed stream. The second problem deals with the formation of corotating shock waves near the leading edge of a broad stream resulting from the merging of characteristic curves. Corotating shocks do not necessarily occur in pairs; a reverse shock can be formed without a forward shock nearby.