A method for regulating the speed of rotation, referred to as speed NR, of at least one main rotor of a multi-engine rotorcraft in the event, referred to as "enginefailure situation", of failure of one of the main combustion engines (2, 3) of a power plant supplying the rotorcraft with the mechanical power necessary at least to drive the main rotor in rotation, the rotorcraft being equipped: with at least one manual flight control member (12, 13) generating, as a result of being driven by a human, manual flight commands which bring about a variation in the pitch of the blades of said at least one main rotor, and with an autopilot which generates automatic flight commands (CA1, CA2) which bring about a variation in the pitch of the blades of said at least one main rotor, the main rotor, when not in an engine-failure situation, being driven by the power plant in accordance with the application of a speed setpoint, referred to as setpoint NR (19, 19'), the value of which is calculated to be variable by a control unit depending on the current flight conditions of the rotorcraft within a range of values of the setpoint NR which are proportional to the value of a predefined nominal speed (NRnom) of driving of the main rotor, the control unit supplying the setpoint NR (19, 19') to a regulating unit for regulating the individual operation of the main engines (2, 3) for driving the main rotor at a speed NR which is in accordance with the setpoint NR (19, 19'), the regulating unit in an engine-failure situation applying a regulation rating, referred to as "OEI rating", regulating the operation of the main engine (2, 3) which remains operational, said OEI rating being selected and applied by the regulating unit from among a plurality of predefined OEI ratings depending on an identified flight phase of the rotorcraft, characterised in that the method comprises the following operations: - an engine-failure situation being identified by the regulating unit, the regulating unit applies said OEI rating and transmits to the control unit data, referred to as "engine-failure data", relating to the identification of the engine-failure situation by the regulating unit, then - following receipt by the control unit of said engine-failure data, the control unit generates said setpoint NR depending on a value which is at least equal to the value of said nominal speed (NRnom), and - in an unfavourable flight situation in which the value of the current speed NR is less than the value of the nominal speed (NRnom), a computer iteratively calculates a speed of driving the main rotor, referred to as target speed (NRobj), as follows: - identification, depending on the current flight situation of the rotorcraft, on one hand of the mechanical power available which is capable of being supplied by the power plant in accordance with the current OEI rating and on the other hand of the current lift provided by the main rotor, then - identification of a maximum lift capable of being provided by the main rotor on condition of stabilised lift of the rotorcraft being obtained, based on a speed NR capable of being achieved within as short a time span as possible from the current speed NR to the target speed (NRobj), then in the event that the value of the current speed NR is less than the target speed (NRobj), generation by the autopilot of automatic flight commands which bring about a variation in the pitch of the blades of the main rotor until driving of the main rotor at said target speed (NRobj) is obtained. with at least one manual flight control member (12, 13) generating, as a result of being driven by a human, manual flight commands which bring about a variation in the pitch of the blades of said at least one main rotor, and with an autopilot which generates automatic flight commands (CA1, CA2) which bring about a variation in the pitch of the blades of said at least one main rotor, - an engine-failure situation being identified by the regulating unit, the regulating unit applies said OEI rating and transmits to the control unit data, referred to as "engine-failure data", relating to the identification of the engine-failure situation by the regulating unit, then - following receipt by the control unit of said engine-failure data, the control unit generates said setpoint NR depending on a value which is at least equal to the value of said nominal speed (NRnom), and - in an unfavourable flight situation in which the value of the current speed NR is less than the value of the nominal speed (NRnom), - identification, depending on the current flight situation of the rotorcraft, on one hand of the mechanical power available which is capable of being supplied by the power plant in accordance with the current OEI rating and on the other hand of the current lift provided by the main rotor, then - identification of a maximum lift capable of being provided by the main rotor on condition of stabilised lift of the rotorcraft being obtained, based on a speed NR capable of being achieved within as short a time span as possible from the current speed NR to the target speed (NRobj), then