We analyze models of quark matter appropriate to the description of matter at densities found within neutron stars. We consider in detail two models: quantum chromodynamics with a bag constant B = 56 MeV/fm/sup 3/, and quantum chromodynamics with B = 0. Both models are consistent with the strength of the quark-quark force found in high-energy particle phenomenology. The pressure, energy density per baryon, and baryon density are calculated. An interesting prediction of our models is that a quark star should have strangeness comparable to its baryon number.