The methods of thermally stimulated currents (TSC) together with low frequency dielectric spectroscopy (LFDS) are combined for the first time to study percolation phenomena. These take place within oil-resin mixtures which constitute conductor/insulator-like composite systems. Each of these techniques is shown to describe selectively one of two different kinds of relaxation processes in the oil component: first, anelastic dipolar movements and second, the circulation of free charges. The separate qualitative interpretations of the combined TSC/LFDS experiments lead to convergent estimations of the percolation thresholds of the two basic materials in oil-resin mixtures. The latter appear as critical concentrations for which the dielectric relaxation processes either comply suddenly with compensation laws or pre-existing compensation phenomena change in nature.