The device according to the invention for charging a first electrical energy storage element (1), in particular an ultracapacitor, from a second electrical energy storage element (2), in particular a battery, is of the type of those comprising a reversible DC/DC converter (3) arranged between the first and second elements (1,2). In accordance with the invention, the device moreover comprises a stepdown voltage converter (4) arranged between the DC/DC converter (3) and the first element (1). Advantageously, the device comprises means controlled (11,12,23) so as to charge with a low current the first element (1) from the second element (2), in particular a battery in a poor state of charge, so as to allow the starting of an engine of a motor vehicle even from a battery in a poor state of charge.