We study a model of three microbial populations competing for three complementary nutrients in a single chemostat. By using methods of numerical bifurcation theory we analyze the model equations and determine the effect of the model parameters on the dynamics of the system. The main question to be answered is whether there exist conditions under which the three populations can coexist in a stable state in the chemostat. The analysis shows that coexistence can be obtained as a stable steady state but also as a stable periodic state for a wide range of operating conditions of the chemostat.