We propose a hybrid maintenance policy which combines periodic (age-based or time-based) regulation-based inspections with aperiodic condition-based inspection/replacements for a stochastically and gradually deteriorating system. The stationary laws of the deterioration state of the maintained system are derived in order to evaluate the long-run average running cost on an infinite span generated by the proposed combined policy. A computable expression of the average cost is established using the regenerative or semi-regenerative properties of the stochastic process describing the maintained system state. The behavior of the proposed maintenance is illustrated through numerical experiments and it is shown that the cost incurred by the optimized combined policy is lower than the cost generated by the regulation-based maintenance alone.