Human diseases such as various types of cancer or autoimmune diseases are at least in part associated with an aberrant regulation of signal transduction pathways. To understand the appearance of these diseases and to develop effective intervention strategies, it is necessary to understand the functioning of the signalling pathways under both, healthy and abnormal conditions. Here, two signalling pathways that depend on the mechanism of regulated proteolysis are considered: i) the canonical Wnt/beta-catenin pathway and ii) the non-canonical NF-kappa B signalling pathway. Theoretical approaches are used to gain deeper insights in their functioning. Mathematical models are developed that take into account the molecular processes of the pathway's core components. Using sets of differential equations, the dynamical properties of the pathway components are investigated. The Wnt/beta-catenin pathway is analysed with respect to the impact of cell-type-specificity, the effects of distinct mutations observed in cancer, and effects of pathway-specific inhibitors. The analyses allow predicting effective target processes for drugs. Regarding the non-canonical NF-kappa B pathway, the first mathematical model is developed that represents experimental findings under wild-type conditions. It offers a mechanistic explanation of experimental observations of many mutations.