This thesis describes a methodology for the requirements analysis of critical real-time systems. The methodology is based on formal methods, and provides a systematic way in which requirements can be analysed and specifications produced. The proposed methodology consists of a framework with distinct phases of analysis, a set oftechniques appropriate for the issues to be analysed at each phase of the framework, a hierarchical structure of the specifications obtained from the process of analysis, and techniques to perform quality assessment of the specifications. The phases of the framework, which are abstraction levels for the analysis of the requirements, follow directly from a general structure adopted for critical real-time systems. The intention is to define abstraction levels, or domains, in which the analysis of requirements can be performed in terms of specific properties of the system, thus reducing the inherent complexity of the analysis. Depending on the issues to be analysed in each domain, the choice of the appropriate formalism is determined by the set of features, related to that domain, that a formalism should possess. In this work, instead of proposing new formalisms we concentrate on identifying and enumerating those features that a formalism should have. The specifications produced at each phase of the framework are organised by means of a specification hierarchy, which facilitates our assessment of the quality of the requirements specifications, and their traceability. Such an assessment should be performed by qualitative and quantitative means in order to obtain high confidence (assurance) that the level of safety is acceptable. In order to exemplify the proposed methodology for the requirements analysis of critical real-time systems we discuss a case study based on a crossing of two rail tracks (in a model railway), which raises safety issues that are similar to those found at a traditional level crossing (i.e. rail-road).