Abstract: According to the invention, during a phase in which the engine is cold-started, the mechanical power supplied by the engine (1) to an auxiliary (23) is reduced by comparison with that normally absorbed by the auxiliary in normal operation. When this auxiliary is an alternator, the reduction in the power supplied by the engine, and therefore the slightest pollution which accompanies it, may be obtained by reducing the excitation current (i) of the alternator, under the control of a computer (11).

Abstract: The heated catalytic converter (1) is placed upstream of a three-way catalytic converter (2) in the outlet line (3) of the exhaust gases. The computer (7) comprises means for the closed-loop regulation of the air/fuel mixture supplied to the engine and means for implementing the method for monitoring the effectiveness of the three-way converter (2). According to the invention, when the engine is being started from cold, means for the closed-loop regulation of this mixture are activated when the temperature of the heated converter exceeds a predetermined temperature (T.sub.S) and insufficient effectiveness of the heated catalytic converter is deduced from the appearance of any fluctuation in the output signal of the probe.