A fuel supply device includes a fuel supply pipe receiving fuel at a non-regulated pressure delivered by a pump, a device for measuring the flow rate of fuel in the pipe, a first controlled variable-restriction valve mounted in the supply pipe, a control system connected to the flow rate measurement device and to the first valve to control the valve to deliver fuel to the engine at a desired flow rate under normal operating conditions of the engine, a second controlled variable-restriction valve mounted in the supply pipe in series with the first valve, and a control for controlling the second valve to enable the engine to be supplied with fuel at an adjustable, reduced flow rate in response to detecting over-speed or over-thrust of the engine.