We analyze a detailed activated sludge model to determine the boundaries for proliferation of flee formers during aerobic or anoxic selection and with soluble or solid substrates. The analysis of competition with several filamentous species shows that the outcome is similar to that of competition with a single species. For the two-species competition we present a general procedure for determining the boundaries of desired operation and compute these boundaries for a slightly modified version of the AEROFIL model (Kappeler and Gujer, 1994a, b Water Resources 28, 303-322). To achieve high conversions in aerobic reactors a substrate concentration gradient should be established implying that the recycle ratio and the sludge-age should be sufficiently small while the dissolved oxygen concentration should be sufficiently large. The analysis of two mixed aerobic reactors suggests that the selector volume should be comparable or larger than that of the reactor. Analysis of an anoxic selector coupled with an aerobic reactor showed that good selection can be obtained with small selectors and a sufficiently large recycle ratio. A control mode based on switching between these two regimes has been suggested. Sustaining the growth of flee formers on a solid-substrate feed that undergoes hydrolysis is a difficult task if the kinetic parameters of the hydrolyzed and soluble substrate are similar. This subject requires further experimental and modeling efforts to account for better selection that has been observed with solid substrates.