We examine how the structure of coplanar MHD fast and slow shocks depends upon the relative magnitudes of the dissipation coefficients contained in classical magnetohydrodynamics. We will use an asymptotic method in which the scale lengths for resistivity, thermal conduction, and viscosity are widely separated and will study the qualitative dependence of the shock solutions upon the ordering of the scales. This method may also be called that of nested subshocks. We define upper limit Mach numbers, for both fast and slow shocks, at which resistivity and thermal conduction taken together can provide all the shock dissipation and at which viscosity is not needed. ¿ American Geophysical Union 1988