The rho-calculus integrates in a uniform and simple setting first-order rewriting, rho-calculus and nondeterministic computations. Its abstraction mechanism is based on the rewrite rule formation and its main evaluation rule is based on matching modulo a theory T . We have seen in the first part of this work the motivations, definitions and basic properties of the rho-calculus. This second part is first devoted to the use of the rho-calculus for encoding a (conditional) rewrite relation. To this end we...