This paper deals with the design of observers that are aimed at dealing with the uncertainty related to the kinetics parameters of chemical and biochemical process models. Two approaches are proposed. The first approach is based on extended Luenberger observer design in which the unknown (kinetic) parameters are used as extra design parameters in order to guarantee zero steady-state observation error of the estimated process variables. The second approach includes the on-line estimation of the unknown (kinetic) parameters in an adaptive observer framework. The stability and convergence of both observers are analysed and their performance is illustrated in numerical simulations.