The stochastic behaviour of an intermittently used system is analyzed in this thesis. Specifically the following measures are derived. i) The distribution of the first disappointment time. ii) The expected number of occurrences of the disappointments during (o,t) iii) The probability that the system is under particular state. iv) The steady-state availability. A intermittently used system is classified into several models according as how a failure occurs and a need acts. Markov renewall process technique is employed to obtain above measures.