In this paper a maintenance policy is optimised for a two-unit system with a parallel structure and stochastic dependences. Monitoring problems are taken into account in the optimisation scheme: the failure time of each unit can be not detected with a given probability. Conditions on the system parameters (unit failure rates) and on the non-detection probabilities must be verified to make the optimisation scheme valid. These conditions are clearly identified. Numerical experiments allow to show the relevance of taking into account monitoring problems in the maintenance model.