The nuclear-matter equation of state is studied with a momentum-dependent effective interaction. The incompressibility and the zero-temperature optical potential are calculated analytically. The momentum distribution of nucleons is examined and the effect of the momentum dependence on pion-production rates is illustrated. The phase transition to a quark-gluon plasma, described by a bag-model equation of state, is studied in an approximation suitable for infinite nuclear matter. PACS number(s): 25.75.+r, 21.65.+f