Highlights•Selection of PHA-storing biomass on fermented municipal WW in a CSTR was studied.•Similar PHA-storage capacity and microbial communities in CSTR vs. feast-famine SBR.•CSTR more efficient in terms of substrate to biomass conversion yields than SBR.•High PHA content and selection ofComamonassp. under excess of P and N.•Low PHA content and selection ofunknown Rhodobacteraceaesp. under N-limitation.