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A new hardware-software reliability model is developed where lifetimes and repair times of the software subsystem have general system state-dependent distributions. The hardware subsystem constitutes an independent alternating renewal process having exponential up-times and general down-times. Multiple errors may be introduced or removed through repairs. The model is formulated as a multivariate stochastic process. To study the performance of the software subsystem under the influence of hardware failures, expressions of various time dependent performance measures are derived. Using the matrix Laguerre transform of U. Sumita (1984), corresponding computational procedures are also developed. A numerical example is given demonstrating the speed, accuracy, and stability of these procedures.