The singularity theory is combined with continuation techniques to classify the static and dynamic behavior in a chemostat involving the competition between plasmid-bearing and plasmid-free cell populations. The analysis of the static bifurcation allows the derivation of analytical conditions for the coexistence of the competing populations and for the safe operation of thebioreactor. The analysis of dynamic bifurcation, on the other hand, shows the ability of the model to predict the coexistence of the two populations in a state of stable limit cycle. Analytical conditions with respect to any growth kinetics are derived for the occurrence of Hopf points in the model. The combination of results of both static and dynamic bifurcation helps to construct a useful picture, in the multidimensional parameter space, of the different behavior predicted by the model.