A method for managing an engine failure on a rotary-wing aircraft, said aircraft comprising: - a hybrid power plant provided with at least two heat engines (13, 13'), at least one electric machine, a main power transmission gearbox and at least one electronic control unit EECU (19, 19'), each electronic control unit EECU (19, 19') being connected to a heat engine (13, 13'), each heat engine (13, 13') being capable of delivering at least a Maximum Continuous Power MCP and OEI 30", OEI 2' and OEI cont contingency powers, said hybrid power plant delivering a total driving power W T to said main power transmission gearbox, - at least one storage means for electrical energy, and - at least one main rotor which is driven, in flight, at an instantaneous speed of rotation Nr by said hybrid power plant, characterised in that - during a checking step, the operation of each heat engine (13, 13') is checked during each flight by means of said electronic control unit EECU (19, 19'), in order to detect any failure of at least one heat engine (13, 13'), a heat engine (13, 13') having failed when at least one other heat engine (13, 13') implements said contingency powers, - during a monitoring step, a monitoring value relating to at least one monitoring parameter of said aircraft and a detection threshold for a deficit of said total power W T are determined, then a comparison is made by comparing said monitoring value with said detection threshold in order to identify a risk of a deficit in said total power W T, said deficit in the total power W T appearing whenever at least one heat engine (13, 13') has to deliver a power greater than a predetermined power W P, and - during a control step, when a failure of at least one heat engine (13, 13') is detected and said detection threshold is exceeded, said electric machine is controlled to deliver an auxiliary power W e so that said total driving power W T of said hybrid power plant is sufficient to manoeuvre said aircraft safely, each heat engine (13, 13') which remains operational not delivering a power greater than said predetermined power W P. - a hybrid power plant provided with at least two heat engines (13, 13'), at least one electric machine, a main power transmission gearbox and at least one electronic control unit EECU (19, 19'), each electronic control unit EECU (19, 19') being connected to a heat engine (13, 13'), each heat engine (13, 13') being capable of delivering at least a Maximum Continuous Power MCP and OEI 30", OEI 2' and OEI cont contingency powers, said hybrid power plant delivering a total driving power W T to said main power transmission gearbox, - at least one storage means for electrical energy, and - at least one main rotor which is driven, in flight, at an instantaneous speed of rotation Nr by said hybrid power plant, - during a checking step, the operation of each heat engine (13, 13') is checked during each flight by means of said electronic control unit EECU (19, 19'), in order to detect any failure of at least one heat engine (13, 13'), a heat engine (13, 13') having failed when at least one other heat engine (13, 13') implements said contingency powers, - during a monitoring step, a monitoring value relating to at least one monitoring parameter of said aircraft and a detection threshold for a deficit of said total power W T are determined, then a comparison is made by comparing said monitoring value with said detection threshold in order to identify a risk of a deficit in said total power W T, said deficit in the total power W T appearing whenever at least one heat engine (13, 13') has to deliver a power greater than a predetermined power W P, and - during a control step, when a failure of at least one heat engine (13, 13') is detected and said detection threshold is exceeded, said electric machine is controlled to deliver an auxiliary power W e so that said total driving power W T of said hybrid power plant is sufficient to manoeuvre said aircraft safely, each heat engine (13, 13') which remains operational not delivering a power greater than said predetermined power W P.