The Jak/Stat1 signalling pathway is a prototypical example of a direct signal transduction system which relays external signals directly from the receptor located at the cellular membrane to its nuclear target genes. This work seeks to acquire a comprehensive theoretical understanding of the quantitative and qualitative aspects of Jak/Stat1 signal transduction, using a combination of different theoretical approaches and methods together with specific experimental measurements. This thesis consists of three independent parts. In part I the biological system is introduced and a detailed model of Jak/Stat1 signalling is presented. The estimation of the model parameters is demonstrated. The model structure and the parameter values are verified using independent experimental measurements. Using numerical model simulations we investigate the dynamics of Stat1 signalling and examine the control properties of the system processes. Part II of this thesis presents a general treatment of Jak/Stat signal transduction using analytical methods. We reduce the complexity of the detailed Jak/Stat model and obtain a simplified linear core model. Using this core model we derive a relation between the lifetimes of the subcellular Stat fractions and their steady state concentrations. Furthermore we model general signal transduction systems as networks of linear state transitions and derive a rule relating the distribution of control among the network processes with the steady state occupancy of the specific network states. In the third part of this work the theoretical predictions of part I and II about the control properties of the subcellular transport processes of the Stat1 molecules are examined using experimental data from different Stat1 transport mutants. The changed phenotypes of these mutant proteins are compared to different model simulations. The high regulatory potential of the shuttling process of inactive Stat1 protein predicted by the model is confirmed.