Temperature anisotropy is a persistent feature of many space plasmas (e.g., the magnetosheath) and can result in significant modifications to the jump conditions at various discontinuities. The effect of anisotropy on the Rankine-Hugoniot (RH) relations is reexamined and the topological changes in the solutions are illustrated by means of a graphical technique. A class of slow shocks is found with quite unusual properties. In particular, there exists a class of nonswitchoff slow shocks which rotate the transverse component of the magnetic field. To distinguish these new solutions from the usual solutions, they are termed anomalous slow shocks. ¿ American Geophysical Union 1995