A stable adaptive control strategy is suggested for a class of continuous-flow bioreactor processes described by Monod kinetics with two unknown parameters, one of which appears nonlinearly. Similarly, as in the case of the previously reported adaptive controllers, the parametrization of the process model, in conjunction with the adaptive exponential feeding strategy and corresponding adaptive algorithms, results in a stable system in which the convergence of the output errors to zero is guaranteed. In the former however, two major problems are encountered : (1) both output errors were used to adjust the controller parameters, which may yield unacceptable performance of the resulting adaptive system; (2) conditions under which the process output can assume only positive values are difficult to derive. Hence, a design of a stable adaptive controller is suggested whose parameters are adjusted using only one of the output errors and that yields acceptable performance of the control system. With this method, conditions under which the process outputs can assume only positive values can be readily derived. These conditions in turn guarantee that the control input saturation at value zero cannot occur. In this context, two adaptive controllers are suggested, such that the resulting adaptive systems are stable and the control objective is met. The adaptive controller design relies on a convenient coordinate transformation, while the proof of stability is based on suitably chosen Lyapunov functions. The performance of the adaptive system is evaluated through computer simulations.