A current problem in biology is how to find adequate models for the dynamics of gene regulatory networks. Recent technological advancements allow for the measurement of gene mRNA levels, in a population of cells, over a period of time. Given a particular gene regulatory network, time series for its components, and a parametrizable mathematical model, optimization algorithms may be used to fit the model's parameters to the observed dynamics. This is useful for validating both the hypothetical network and its model, and for providing new insights about the underlying biological system. In this thesis I analyze two case studies: the SOS DNA damage repair network in E. coli and a hypothetical network for the transcriptional regulation of the gene Flr1's response to oxidative stress in yeast, induced by the drug Mancozeb. For the SOS network, I use a known piecewise-linear model and the parameter inference algorithm BFGS. I compare two adaptations of piecewise linear models, obtaining a general form that encompasses both, and I describe a new version of an optimization algorithm that may be used for inferring parameters in that model. These results are applied to the Flr1 network. Both models are used to extract information that is confirmed by biological literature.