For microbial species competing for one limiting resource in a chemostat, mathematical models and in particular the competitive exclusion principle (CEP) predicts survival of only one species in any case. Quantitative experimental data from our model system related to genetic disease Cystic Fibrosis alludes to the coexistence of at least two competing species. We developed a new mathematical model (extension of the classical chemostat) to comply with the experimental phenomena by including species specific properties of the microorganisms of concern. We will present the mathematical tools and the analysis fo the mathematical model, consisting of a four-dimensional system of nonlinear ordinary differential equations as well as computed simulations for experimental data. We found that the dynamic of the system changes in a fundamental way, if interspecific competition is included; a Hopf bifurcation occurs for an appropriate choice of parameters. Experimental data serve as basis of knowledge for the applied assumptions. These are a) one species produces a secondary metabolite, b) the metabolite has a growthinhibiting effect, but can also be exploited as a secondary carbon resource, c) some of the species could compete directly (e.g. via toxin production), and d) a lethal inhibitor could be introduced that cannot be eliminated by one of the species and is selective for the stronger competitor.