  We discuss various examples of classical Calogero-Moser models with internal
degrees of freedom. These models besides of having some attractive properties,
like the complete integrability, are of interest eg., in studying spectral
properties of quantum chaotic systems. The role of internal degrees of freedom
is important in at least two aspects. Firstly, they come in play as dynamically
evolving couplings between repelling pairs of eigenvalues, hence they influence
the speed of eigenvalue dynamics. Secondly their initial values determine the
"reachable sets" of couplings between particular pairs accessible during the
evolution. The considered models are studied in a framework of matrix dynamics
in a unifed way based on a reduction of a linear model in an extended
phase-space. Such an approach enables showing an equivalencies among various
types of similar models employing "vectorial degrees of freedom" and
constructing new systems of similar type.
