Resource-based competition between microorganisms species in continuous culture has been studied extensively both experimentally and theoretically, mostly for bacteria through Monod and and Contois "constant yield" models, or for phytoplankton through the Droop "variable yield'' models. For homogeneous populations of N bacterial species (Monod) or N phytoplanktonic species (Droop), with one limiting substrate and under constant controls, the theoretical studies indicated that competitive exclusion occurs: only one species wins the competition and displaces all the others. On the contrary for attached bacterial species described by a Contois model, theory predicts coexistence between several species. In this paper we present a generalization of these results by studying a competition between these three different types of microorganisms. We prove that the outcome of the competition is a coexistence between several attached bacterial species with a free species of bacteria or phytoplankton, all the other free species being washed out. This demonstration is based mainly on the study of the substrate concentration's evolution.