The effects of dissipation on rotational discontinuities have been studied as an initial-value problem. Starting with a rotational discontinuity, we apply resistivity and viscosity and follow the resulting evolution of the system by numerically integrating in time the viscous, resistive MHD equations. The results show that by including dissipation, a rotational discontinuity is unstable and will evolve to an MHD intermediate shock of the kind whose shock frame fluid velocities are subfast, super-Alfv¿nic, and superslow behind the shock. (However, with small dissipation, the intermediate shock and the rotational discontinuity would be very close.) The results also show that there are a larger class of shocklike structures, which do not satisfy Rankine-Hugoniot relations, in the time-dependent dissipative MHD equations. The results also indicate that the corresponding Riemann problem is not well-posed. In addition, the admissibility of MHD equations is discussed. The conclusion is that all entropy satisfying shocks along the shock curve are physical. This differs from the conventional view that intermediate shocks are not allowed. This also differs from the admissibility criterion of Oleinik [1957> and Lin [1981>. However, their criterion is valid for a strictly hyperbolic system, whereas the set of MHD equations is nonstrictly hyperbolic. Regarding the magnetospheric physics, our study suggests that instead of rotational discontinuities, intermediate shocks should exist at the magnetopause. Thus one has a different signature from that of a rotational discontinuity to compare with space observations. The results also provide an explanation for the observation that the sense of the magnetic field rotation across the magnetopause depends on the relative orientation of the magnetosheath and the magnetospheric field, and the rotation is less than 180¿. ¿ Amercian Geophysical Union 1988