Signatures of series and parallel systems consisting of non disjoint modules

System signature is a useful tool to analyze coherent systems. In reliability theory, a large number of systems is actually the composition of disjoint subsystems (modules). However, in real life, there are situations in which the subsystems have common components. In this article, we consider the problem of obtaining signatures as well as minimal signatures of series and parallel systems that are composed of subsystems sharing a component. That is, these subsystems are no longer disjoint. Computational results are also presented to illustrate our findings.