Method for adjusting the fuel flow of a fuel pump drawing fuel from a fuel tank and fuel pump for such a method

The method involves sucking fuel from a fuel tank for delivery to an internal-combustion engine. A fuel pump unit has twp pump stages where below a certain supply pressure in a discharge opening (25) of the fuel pump unit the two pump stages are parallel and above a certain supply pressure they are serially switched. The first pump stage possesses a suction connection (7) connected with a fuel tank (8) and has a pressure connection (22). The second pump stage has a suction connection (17, 28) and a pressure connection (32) leading to the discharge opening (25) of the fuel pump unit, as well as with a two-way valve (13), which switches between positions.