A problematic feature in most fermentation processes is that on-line measurement of the most important biological process variables, the concentration of the bio-mass and its specific growth rate, cannot be directly measured. An approach for estimating these biological variables and for controlling the specific growth rate in a continuous flow bioprocess of a stirred tank reactor is presented and analysed. The goal in the control is to get the specific growth rate to track the rate of a given reference model, A dynamic model for the specific growth rate is obtained from the general growth and substrate consumption model. The structure of the rate model is then applied in the reference model structure. The methodology studied is based on two issues, joint state and parameter estimation and direct adaptive control. From the theoretical viewpoint, this forms a combination of indirect and direct adaptive control. The structure of the control law is justified by the structure of the law obtained for known fixed parameters. Convergence of the estimation scheme and of the adaptive control scheme are demonstrated via Lyapunov's method, and separately. The choice of the appropriate Lyapunov function results in a Pl-type controller with the gains as the parameters to be adjusted by the user. A simulation study based on Monod's model and time-varying model parameters and subject to measurement noise shows the feasibility and robustness of the adaptive control methodology developed for this non-linear process.