The electrical impedance and the optoelectrical impedance due to electron-hole recombination in the depletion layer and at the surface of a semiconductor electrode are calculated. It is shown that both types of impedance follow from a common formula for the ac recombination current density in the external circuit, which is derived from first principles. It is found that both the electrical and optoelectrical impedance methods provide the same information about recombination. Both methods enable one to distinguish surface recombination from recombination in the depletion layer. The theoretical results are compared with the electrical and optoelectrical impedance results measured at GaAs and CdS photoanodes.