In modern society, systems composed of many components which may interact with each other play a vital role and become more and more important. It is not a simple task to ensure the normal operation of systems since that they are often subject to deterioration and wear and operate in a changing environment. Maintenance actions can be carried out in order to avoid the failure of the system.This thesis considers maintenance problems and reliability evaluations of multi-component systems. At first, we study a two-component system with various types of stochastic dependencies. Three models have been considered. For each of the three models above, several maintenance policies are proposed. Under each policy, the explicit expressions of the long-term average cost as well as the cost optimality are studied. In addition, for the last two models, several guarantee policies are proposed and the allocation of the warranty cost between the manufacturer and the consumer are studied.Finally, an M-out-of-N system which operates in a dynamic environment is studied. Performance measures such as the reliability of the system, the remaining useful life (RUL), the asymptotic availability are calculated.In conclusion, it is shown that in multi-component systems, stochastic dependence between components may affect both system performance measures and the optimization of maintenance policies