The cumulative microslip phenomenon is the accumulation of relative slips in a tangential direction on the contact interface of two solids under cyclic loadings. This lead to significant global relative displacement between components and can account for the failure of some assembly parts in mechanical structures. Practical examples from the automotive industry are presented in this paper to describe the cumulative microslip in real situations. The phenomenon is then discussed from a theoretical point of view as an asymptotic behaviour by analogy with the ratchetting effects in elastoplasticity. Accommodation and slip shakedown are introduced in the same spirit. A slip shakedown theorem is proposed and leads to the definition of a safety coefficient with respect to slips when a standard law of friction is assumed. The safety coefficient can be computed from two static and kinematic approches in min-max duality. A simple example is given.