The evolution of rotational discontinuities (RDs) is followed using a hybrid numerical code. An extensive parameter variation is carried out, with particular emphasis on &bgr;, Ti/Te, &thgr;B (the angle between the normal and total magnetic field), and the helicity of the RD. The RD structure is shown to have features in common with the evolution of both strongly modulated, nonlinear wave packets and linear dispersive wave propagation in oblique magnetic fields. For small &thgr;B, the RD disperses linearly giving fast Alfv¿n waves upstream and downstream, respectively, and the familiar S-shaped hodograms. At larger &thgr;B(≈30¿), nonlinearity becomes important and strong coupling to a compressional (sonic) component can occur in the main current layer. When the ions are cold, there is a critical value of &bgr;e(=&bgr;*) when the intermediate wave train moves from the downstream side of the RD to the upstream and is replaced on the downstream side by slow modes. This is reflected in the hodograms by a change of the wave polarization on both sides, and represents an important modification to the original Goodrich and Cargill (1991) wave model of RDs. As Ti/Te increases, the spreading rate of the current layer increases for moderate &thgr;B. For large &thgr;B(≈60¿), RDs with electron (ion) sense of rotation show increased (decreased) spreading with increasing Ti/Te. These results are applied to RDs observed in the solar wind and at the magnetopause. ¿ American Geophysical Union 1993