This thesis consists of two independent contributions. The rst deals with model checking of reference passing systems, and the second considers diagnosability under the weak fairness assumption. Reference passing systems, like mobile and recon gurable systems are everywhere nowadays. The common feature of such systems is the possibility to form dynamic logical connections between the individual modules. However, such systems are very di cult to verify, as their logical structure is dynamic. Traditionally, decidable fragments of -calculus, e.g. the well-known Finite Control Processes (FCP), are used for formal modelling of reference passing systems. Unfortunately, FCPs allow only `global' concurrency between processes, and thus cannot naturally express scenarios involving `local' concurrency inside a process. This thesis proposes Extended Finite Control Processes (EFCP), which are more convenient for practical modelling. Moreover, an almost linear translation of EFCPs to FCPs is developed, which enables e cient model checking of EFCPs. In partially observed systems, diagnosis is the task of detecting whether or not the given sequence of observed labels indicates that some unobservable fault has occurred. Diagnosability is an associated property, stating that in any possible execution an occurrence of a fault can eventually be diagnosed. In this thesis, diagnosability is considered under the weak fairness (WF) assumption, which intuitively states that no transition from a given set can stay enabled forever - it must eventually either re or be disabled. A major aw in a previous approach to WF-diagnosability in the literature is identi ed and corrected, and an e cient method for verifying WF-diagnosability based on a reduction to LTL-X model checking is presented.