Molecular dynamics simulations have been performed for highly compressed fluid hydrogen in the density and temperature regime of recent shock-compression experiments. Both density functional and tight-binding electronic structure techniques have been used to describe interatomic forces. Two tight-binding models of hydrogen have been developed with a single s-type orbital on each atom that reproduce properties of the dimer, of various crystalline structures, and of the fluid. The simulations indicate that the rapid rise in the electrical conductivity observed in the gas-gun experiments depends critically on the dissociated atoms(monomers). Hugoniots derived from the equations-of-state of these models do not exhibit the large compressions predicted by the recent laser experiments. ©2000 American Institute of Physics.