Understanding the dynamical behavior of biological networks is complicated due to their large number of components and interactions. We present a method to analyse key processes for the system behavior, based on the a priori knowledge of the system trajectory and the simplification of mathematical models of these networks. The method consists of the model decomposition into biologically meaningful processes, whose activity or inactivity is evaluated during the time evolution of the system. The structure of the model is reduced to the core mechanisms involving active processes only. We assess the quality of the reduction by means of global relative errors and apply our method to two models of the circadian rhythm in Drosophila and the influence of RKIP on the ERK signaling pathway.