The role of atomic cooperation in producing optical bistability in a system consisting of resonant atoms in a low-Qcavity driven on resonance is investigated. It is shown that while completely correlated atomic cooperation precludes steady-state bistability, the assumption that each atom behaves independently and is affected only by the average behavior of the others leads to a bistable steady state. Certain physical and mathematical aspects of the two kinds of cooperation are discussed, and the relationship of the results to the problem of optical bistability without a resonator is indicated.