The focus of this paper is two-fold: (1) to examine how the presence of the spiral magnetic field affects the evolution of interplanetary corotating solar wind streams, and (2) to ascertain the nature of secondary large-scale phenomena likely to be associated with streams having a pronounced three-dimensional (3-D) structure. The dynamics are presumed to be governed by the nonlinear polytropic, single-fluid, 3-D MHD equations. Solutions are obtained with an explicit, Eulerian, finite differences technique that makes use of a simple form of artificial diffusion for handling shocks. For smooth axisymmetric flows, the picture of magnetically induced meridional motions previously established by linear models requires only minor correction. In the case of broad 3-D streams input near the sun, inclusion of the magnetic field is found to retard the kinematic steepening at the stream front substantially but to produce little deviation from planar flow. For the more realistic case of initially sharply bounded streams, however, it becomes essential to account for magnetic effects in the formulation. Whether a full 3-D treatment is required depends upon the latitudinal geometry of the stream. Where the stream front is sharply inclined to the equator or contains signficant substructure, the 3-D effects (the modification to planar flow occasioned by the nonradical motions driven by the interaction) can exceed the magnetic effects. Conventional radial alignment tests may be incapable of distinguishing between 3-D and temporal effects because the former need not be accompanied by readily identifable north-south flow signatures, for example. The shock surfaces predicted by the model can be quite oblique and can extend to latitudes beyond the north-south boundary of the stream. Even with magnetic and 3-D effects accounted for, however, shock formation in the model still occurs much closer to the sun than is generally observed. It is demonstrated how the systematic nonradial flow patterns seen about a stream interface can be used to infer the orientation of the stream front. Estimates of the latitudinal transport of angular momentum flux by stream fronts suggests that the effect is likely to be so large as to preclude accurate measurement of this quantity beyond about 0.5 AU. The 3-D transport may have a discernible influence upon average magnetic field behavior, but steady corotating flows cannot produce the large north-south field deflections commonly observed near 1 AU.