The aim of this paper is to discuss the problem of modelling and optimising condition-based maintenance policies for a deteriorating system in presence of covariates. The deterioration is modelled by a non-monotone stochastic process. The covariates process is assumed to be a time-homogenous Markov chain with finite state space. A model similar to the proportional hazards model is used to show the influence of covariates on the deterioration. In the framework of the system under consideration, an appropriate inspection/replacement policy which minimises the expected average maintenance cost is derived. The average cost under different conditions of covariates and different maintenance policies is analysed through simulation experiments to compare the policies performances.