The problem of dynamical identification of unknown characteristics (states/parameters) in a biochemical model of a fed-batch bioreactor system given observations of some states is considered. An algorithm that solves this simultaneous state and parameter estimation problem and that is stable with respect to bounded informational noises and computational errors is presented. The algorithm is based on the principle of auxiliary models with adaptive controls. Convergence of the algorithm is proven and a convergence rate is derived. The performance of the algorithm is illustrated to a typical single-species bioreactor example.