Maintenance models involving minimal imperfect repair frequently appear in the literature of reliability and operations research. Most of the literatures concerning the stochastic behavior of repairable systems assume that it takes negligible time to repair a failed system and so the length of repair time does not affect the maintenance strategy. It is more realistic to consider the length of repair times in developing maintenance model, however. In this paper, we consider an imperfect repair model with random repair time and investigate some stochastic properties of the number of perfect repairs and the number of minimal repairs. Also we derive the expressions for evaluating the expected numbers of perfect and minimal repairs in general and apply these formulas for certain parametric life distributions.