The analytical method of part I is used to calculate the dependence of composite deformation on cyclic, geometric, and constituent deformation parameters. The calculated hysteresis loop of matrix stress versus temperature caused by plastic deformation stabilizes after a few cycles so that a steady-state plastic compression-tension fatigue results when no external stress is present. In most cases plastic shakedown is thereby precluded. The calculated stresses can be much different from those predicted by existing elasticity analyses. Even when the matrix plasticity is fairly small, the elasticity approaches at best predict the range of, but not the extrema in, component stresses. Failure of a cycled eutectic composite may be due to any of several causes, and all must be considered in any evaluation.