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

Calogero-Moser models with internal degrees of freedom revisited