We present developments concerning the synthesis of single-input, single-output (SISO) and multi-input, multi-output (MIMO) adaptive linearizing algorithms for the operation of bioreactors. Results are illustrated for the baker's yeast fermentation process. The synthesis of these nonlinear control laws is performed by employing differential geometry techniques with system linearization by state feedback. The controller design includes a step of order reduction of the process state model. The adaptive feature comes from the online estimation of the required process time varying parameters. The adaptive algorithm proposed enforces a desired and pre-set second order convergence dynamics. Formulating the estimator on this basis leaves the user with the choice of two simple and intuitive tuning parameters with physical meaning-a damping coefficient and a natural period of oscillation.