The following mechanism of multiple failures in a system is considered. Suppose that the failure of a component eicauses with probability pij ≤ 0 an instantaneous failure of a component eiwhich can, in turn, cause another instantaneous failure of ekwith probability PJk0 and so on (i,j, k = 1, 2,..., n). We apply this mechanism to the Marshall and Olkin formula for the joint probability distribution of system component lifetimes when multiple failures in the system occur. The formulae given replace the Marshall and Olkin constant set failure rates by variable ones. Other comparisons with Marshall and Olkin models are made.