The generalized software reliability model on the basis of nonstationary Markovian system of service is proposed. Approximation by distribution of Cox allows investigating growth of software reliability for any kinds of distribution of time between the moments of detection of errors and exponential distributions of time of their correction. The model allows receiving the forecast of important characteristics: the number of the corrected and not corrected errors, required time of debugging, etc. The diagram of transitions between states of the generalized model and system of the differential equations are presented. The example of calculation with use of the offered model is considered, research of influence of variation coefficient of Cox distribution of duration of intervals between the error detection moments on values of look-ahead characteristics is executed.