A collisionless parallel shock model is presented which is based on solitary-type solutions of the modified derivative nonlinear Schr¿dinger equation (MDNLS) for parallel Alfv¿n waves. We generalize the standard derivative nonlinear Schr¿dinger equation in order to include the possible anisotropy of the plasma distribution function and higher-order Korteweg--de Vries type dispersion. Stationary solutions of MDNLS are discussed. The new mechanism, which can be called ''adiabatic,'' of ion reflection from the magnetic mirror of the parallel shock structure is the natural and essential feature of the parallel shock that introduces the irreversible properties into the nonlinear wave structure and may significantly contribute to the plasma heating upstream as well as downstream of the shock. The anisotropic nature of ''adiabatic'' reflections leads to the asymmetric particle distribution in the upstream as well as in the downstream regions of the shock. As a result, nonzero heat flux appears near the front of the shock. It is shown that this causes the stochastic behavior of the nonlinear waves which can significantly contribute to the shock thermalization. The number of adiabatically reflected ions define the threshold conditions of the fire-hose and mirror type instabilities in the downstream and upstream regions and thus determine a parameter region in which the described laminar parallel shock structure can exist. The threshold conditions for the fire hose and mirror-type instabilities in the downstream and upstream regions of the shock are defined by the number of reflected particles and thus determine a parameter region in which the described laminar parallel shock structure can exist. ¿ American Geophysical Union 1993