The electric Ohm resistivity of electroless Cu depositions on dielectric substrates as a function of their thicknesses is studied. Substantial deviations (up to 10-20 times) from the standard resistivity (rho(infinity) = 1.7 mu Omega cm(-1)) below 0.5 mu m thicknesses are observed. The experimental data show for the entire region of thicknesses (d(infinity) similar to 0.07-5 mu m) a power function between the relative resistivity changes (Delta rho/rho(infinity)) and the inverse thickness of depositions (d(infinity))-(Delta rho/rho(infinity))similar to(1/d(infinity))(0.8). This empirical relation is discussed as an effect of the porous structure of the metallic layers deposited on the substrate. A scanning electron micrography was applied in order to visualize the morphology of the depositions. The micrographs clearly show the evolution of the deposition profile : starting from separate islands at the very beginning of the process, and gradually covering the entire area with continuous but porous metal layers.