  We introduce a particle mechanics model with Sp($2M$) gauge invariance.
Different partial gauge-fixings by means of sl(2) embeddings on the gauge
algebra lead to reduced models which are invariant under diffeomorphisms and
classical non-linear \W-transformations as the residual gauge symmetries thus
providing a set of models of gauge and matter fields coupled in a \W-invariant
way. The equations of motion for the matter variables give Lax operators in a
matrix form. We examine several examples in detail and discuss the issue of
integration of infinitesimal \W-transformations.
