We advance the notion of a classical density matrix, as a classical analogue of the quantum mechanical
statistical operator, and investigate its main properties. In the case of composite systems a partial trace-like
operation performed upon the global classical density matrix leads to a marginal density matrix describing
a subsystem. In the case of dynamically independent subsystems (that is, non-interacting subsystems) this
marginal density matrix evolves locally, its behavior being completely determined by the local phase-space
flow associated with the subsystem under consideration. However, and in contrast with the case of ordinary
marginal probability densities, the marginal classical density matrix contains information concerning the
statistical correlations between a subsystem and the rest of the system.