Three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis are described by a system of differential equations modelling the interaction of microbial populations in a chemostat. The microbes consume and/or produce simple substrates, alcohols and fatty acids, acetic acid, and hydrogen. Acetogenic bacteria and hydrogenotrophic methanogens interact through syntrophy. The model also includes the inhibition of acetoclastic and hydrogenotrophic methanogens due to sensitivity to varying pH-levels. To examine the effects of these interactions and inhibitions, we first study an inhibition-free model and obtain results for global stability using differential inequalities together with conservation laws. For the model with inhibition, we derive conditions for existence, local stability, and bistability of equilibria and present a global stability result. A case study illustrates the effects of inhibition on the regions of stability. Inhibition introduces regions of bistability and stabilizes some equilibria.