The gas-particle flow problem is formulated with the gas and solid particles out of equilibrium with respect to momentum and thermodynamical slip, as well as mass loss from the particle phase. The nonlinear effects are illustrated by the normal shock wave in which the particle phase undergoes relaxation effects following the gas dynamic shock; other nonlinear effects, such as the oblique shock is discussed. These are followed by a thorough discussion of weak wave in terms of higher order waves in Whitham's sense with analogies to waves in a chemically reacting mixture. The wave structures...