Abstract This paper analyses a two-unit cold standby system under two very general sets of conditions : ( i) each unit of the system having three different modes of working, normal, partial failure and total failure ; and ( ii) breakdown of the system occurring when both the units are down and failure occurs when breakdown is not repaired within the allowed down-time. We obtain a Laplace-Stieltjes transform of the distribution of time to system failure, it's mean time and steady state probabilities of the system being in up, down or failed states.