An important problem in reliability theory is to determine the reliability of a complex system given the reliabilities of its components. In real life, the system and its components can be found in a range of states varying from perfect functioning through various levels of performance degradation to complete failure. This paper presents some models and their applications, in terms of reliability analyses, to situations where the system can have a whole range of states and all its components can also have a wide range of multiple states. Properties of the system structure function and computation and approximation of system state probabilities and system reliability measures are given.