An adaptive extremum-seeking control scheme for continuous stirred-tank bioreactors is proposed which utilizes the structure information of the kinetics of bioreactors to construct a seeking algorithm that drives the system states to the desired setpoints that optimize the value of an objective function. Lyapunov's stability theorem is used in the design of the extremum-seeking controller stucture and the development of the parameter learning laws. Numerical simulations illustrate the effectiveness of this approach.