The paper is concerned with dynamical modeling of early and late gene expression in one of Interferon-β induced signaling pathways. First, the biological background is given. Subsequently, the importance of stochastic nature of biological processes is addressed. Then, the assumptions underlying their deterministic modeling are presented and the mathematical model is introduced. Finally, the methodology for identification of model parameters is briefly described, followed by the presentation of experimental and simulation results. In addition to analysis of the particular regulatory network, this work also builds a framework for modeling of other signalling pathways whose not all components are known.