The evolution of magnetohydrodynamic shock waves depends on dissipation properties of the medium. The increase or decrease of dissipation coefficients results in a larger or smaller thickness of fast and slow shocks. This is not the case for trans-Alfv¿nic shock waves (TASWs), i.e., such at which the flow velocity passes through the Alfv¿n velocity. In the present paper, it is shown that the variation of dissipation coefficients may cause disintegration of TASWs or diffusion-like change of their upstream and downstream states. This mechanism is complementary to the accumulation of an Alfv¿n-type perturbation inside the shock transition layer. It is also demonstrated that if this variation has a cyclic nature, the TASW undergoes oscillatory disintegration. In this process, it repeatedly transforms into another TASW and emits a nonlinear wave train consisting of shock and rarefaction waves. The implications for planetary bow shocks and shocks induced by CMEs are discussed. In the observational data the disintegration may show up as an unusual position of the bow shock under typical conditions of the solar wind and as a multiple, time-varying structure of the CME leading edge. ¿ 2000 American Geophysical Union