Studies of rotational discontinuities (RDs) and their role in affecting the magnetic field rotations at the magnetopause have been generally conducted using one-dimensional simulations and for RDs in isolation from external perturbations. The conditions at the magnetopause are, however, often turbulent with large Alfv¿nic and mirror mode fluctuations. Here, previous calculations are extended to two-dimensions using the hybrid code and the effect of external perturbations on the stability of both isotropic and anisotropic RDs is examined for the first time. As in the one-dimensional simulations and in agreement with observations at the magnetopause, RDs are found to satisfy the minimum shear condition (rotation angles less than or equal to 180¿) and have gradient scale half-widths of the order of 1--4 ion inertial lengths. In addition, RDs are found to be quite stable even when large amplitude mirror and Alfv¿n waves impinge upon them. No evidence for two-dimensional (e.g., surface or shear) instabilities were found. Although simulations show the presence of a coherent wavetrain for some of the RDs, the observations of RDs at the magnetopause have not identified any wavetrain. It is shown that under the turbulent conditions prevalent at the magnetopause, the detection of wavetrain in the data would most likely require multispacecraft measurements. ¿ American Geophysical Union 1995