A method or process for producing polyhydroxyalkanoates (PHAs) in biomass. The process entails feeding an organic carbon containing substrate to biomass enriched in PHA accumulating bacteria. Particularly the process entails intermittently supplying the substrate to the biomass at least three separate times over a selected period. The object of the process is to produce PHA having a relatively high molecular weight, at least 400,000 g/mole. By controlling the frequency at which the substrate is supplied to the biomass and by feeding a sufficient amount of the substrate to the biomass, the method or process produces the PHA having the relatively high molecular weight.