Implantable biochemical fuel cells for the operation of heart pacemakers or artificial hearts convert oxidisable body substances such as glucose on the anode side and reduce the oxygen contained in body fluids at the cathode. The anode and cathode are separated by membranes which are impermeable to albumen and blood corpuscles in body fluids. A chemical shortcircuit cannot occur in practice if, according to the invention, one or more selective oxygen electrodes with carbon as catalyst are arranged so that the mixture which diffuses into the cell from body fluids during operation reaches the fuel cell electrode through the porous oxygen electrode. The membranes used must be permeable to water. Cellulose, polymerised polyvinyl alcohol or an ion exchanger with a buffering capacity between pH5 and 8 act as permeable materials.