The aim of this research is to mathematically model enzymatic processes that are used in biocatalysis. This thesis comprises models for two different enzymatic reactions. The first model was used to describe lactose hydrolysis and transgalactosylation by -galactosidase at various initial lactose concentrations and temperatures. Each experiment was considered as an independent estimation of the model parameters, and consequently, model parameters were fitted to each experiment separately. The estimation of the parameters for each individual experiment preserved the time dependence of the set of measurements obtained by the experiment. The software package MATLAB was used in the numerical calculations. The parameters were estimated by the nonlinear least squares method with Genetic Algorithm. The effect of temperature is small compared to the influence of the initial lactose concentration. With one experimental time course, the model can estimate all significant parameters with high accuracy. The second model describes a bi-enzymatic process including an enzymatic regeneration system for NAD(P)H oxidation. The coenzyme regeneration system employs laccase and a number of various redox mediators to oxidize NAD(P)H. Reaction engineering by modeling was used to optimize the employed enzyme, coenzyme and redox mediator concentrations. Glucose dehydrogenase from Bacillus sp. served as a convenient example of the synthetic enzymes that depends either on NAD+ or NADP+. The capability of laccase from Trametes pubescens in combination with acetosyringone or syringaldazine as redox mediator was tested to regenerate (oxidize) the coenzymes. This model also was used to simulate and optimize the employed enzyme, coenzyme and redox mediator concentrations.