A charge and discharge control circuit which accommodates pulsed charge and pulsed discharge and can control charge and discharge of a secondary battery with safety, and a rechargeable power supply device having the same built therein are provided. The charge and discharge control circuit includes a delay time switching circuit for shortening a delay time of overcharge detection after charge inhibition is canceled. When overcharge is detected after the charge inhibition is canceled, the charge is inhibited in a delay time which is shorter than a normal delay time of the overcharge detection.