Many wear processes used for modeling accumulative deterioration in a reliability context are nonhomogeneous Levy processes and, hence, have independent increments, which may not be suitable in an application context. In this work we consider Levy processes transformed by monotonous functions to overcome this restriction, and provide a new state-dependent wear model. These transformed Levy processes are first observed to remain tractable Markov processes. Some distributional properties are derived. We investigate the impact of the current state on the future increment level and on the overall accumulated level from a stochastic monotonicity point of view. We also study positive dependence properties and stochastic monotonicity of increments.