The paper proposes an observability analysis and estimation schemes for specific growth rates for a wastewater treatment process. A 2-stage model of 6 dynamic states is assumed, describing the acidogenesis and methanogenesis of two different populations of microorganisms (acidogenic and methanogenic), and the evaluation of the total carbon dioxide production including the soluble part. The main result is that the specific growth rates of the two populations of bacteria can be stability estimated only from easily measured quantities -- the dilution rate and the flow rates of methane and carbon dioxide in the biogas.