Abstract Specific kinetic rates are key variables regarding metabolic activity in bioprocesses. They are non-linear functions of concentrations and operating conditions and therefore of difficult access for process control. In this paper, a multiple kinetic rates observer based on second-order sliding mode ideas is proposed. The main difference with other proposals is that smooth estimates are achieved in finite-time without adding additional dynamics. The resulting estimator is robust against uncertainty in the model of the estimated variables. Experimental results from continuous fermentation of S. cerevisiae are presented, where microbial specific growth rate and net ethanol production rate are estimated.