In this paper we consider the development of hybrid numerical
methods for the solution of hyperbolic relaxation problems with
multiple scales. The main ingredients in the schemes are a suitable
merging of probabilistic Monte Carlo methods in non-stiff regimes
with high resolution shock capturing techniques in stiff ones. The
key aspect in the development of the algorithms is the choice of a
suitable hybrid representation of the solution. After the
introduction of the different schemes the performance of the new
methods is tested in the case of the Jin-Xin relaxation system and
the Broadwell model.