This paper examines the conditions for the emergence of complex dynamic behavior in systems of pure and simple microbial competition. A general unstructured model for the competition is considered where the specific growth rates of both species are assumed to depend arbitrarily on both the substrate and the biomass. The model also assumes a general dependence of the yield coefficients on the substrate. It is shown that useful analytical conditions can be readily obtained that characterize the occurrence of periodic behavior in the chemostat. These results show that for a number of specific growth rates expressions, the existence of complex behavior is conditioned mainly by the variability of the yield coefficients. In particular, when the two species are assumed to grow following the biomass-dependent Contois model, the analysis uncovered complex behavior including chaos, which is a novelty for time invariant pure and simple microbial competition. (C) 2012 Elsevier Ltd. All rights reserved.