The paper presents on-line estimation strategies for bioprocesses, which are characterized by strongly nonlinear dynamics. A general form for the state observers is analysed and the exponential observability of bioprocesses is discussed. For those biotechnological processes that possess the property of exponential observability, an extended Luenberger observer is implemented. If exponential observers cannot be used, a solution is the design of asymptotic observers. The proposed observers are implemented for a microbial growth process coupled with an enzyme-catalysed reaction, which is a usual bioprocess that takes place in a fed-batch bioreactor. Illustrative computer simulations and conclusions are included.