The Hugoniot equations of state of a large number of representative polymers have been obtained. Two aspects of the results are particularly striking: (1) The u{sub s}(u{sub p}) Hugoniots of all the polymers extrapolate to bulk sound velocities higher than the ultrasonic values, an indication of a rapidly varying rate of change of compressibility in this region. This is attributed both to the two-dimensional nature of polymer compression and to the form of the interchain interaction potential. (2) A relatively high pressure transformation (in the range 20-30 GPa), characterized by a change in slope of the u{sub s}(u{sub p}) Hugoniot and sometime by a large volume change as well, is observed for all of the polymers. This transformation is probably associated with pressure-induced cross bonding. In particular, for those polymers which contain rings in their monomer structure and which display the largest volume change at transformation, it is proposed that carbon-carbon covalent bonds along chains are broken and tetragonal bonds between chains are formed in a manner analogous to the graphite-diamond transformation.