Mechanical system for transmitting rotary motion between at least one engine (2, 2') and at least two separate driven shafts (40, 41) of an accessory gear box, said mechanical system allowing the at least one engine (2, 2') to rotate one of said at least two driven shafts (40, 41) in isolation, or to simultaneously rotate said at least two driven shafts (40, 41) together with at least one rotor (3, 103, 103') of an aircraft, said mechanical system comprising at least one input wheel (8, 8') arranged to be rotated by the at least one engine (2, 2'), each input wheel (8, 8') being arranged to be rotated by a corresponding dedicated engine (2, 2'), and comprising a selective rotary drive member that is axially movable between two separate drive positions: • a first drive position in which one of said engines, of which there is at least one, rotates both said at least one rotor (3, 103, 103') and a first driven shaft of said accessory gear box, and • a second drive position in which one of said engines, of which there is at least one, rotates a second driven shaft of said accessory gear box, said second driven shaft being separate from said first driven shaft, said mechanical system further comprising: • a bevel gear pair having intersecting axes and, made up of a first bevel gear, referred to as a "power gear", that is provided with teeth and is rotatably movable about a first axis, and of a bevel wheel that is provided with teeth and is rotatably movable about a second axis, said respective teeth and of said first bevel gear and said bevel wheel interacting with one another in a complementary manner, said bevel wheel being arranged to rotate said at least one rotor (3, 103, 103'), • a "take-off" shaft that is constantly rotated by said at least one input wheel, said take-off shaft allowing rotary motion to be constantly transmitted to said second driven shaft of said accessory gear box without rotating said bevel gear pair and the accessory gear, in said second drive position of said selective drive member and when said engine rotates said at least one corresponding input wheel, said input wheel rotates said take-off shaft and said second driven shaft of said accessory gear box, characterised in that said mechanical system comprises a second bevel gear, referred to as an "accessory gear", that is provided with teeth that mesh with the teeth of said bevel wheel, said accessory gear being arranged to transmit rotary motion to said first driven shaft of said accessory gear box, said take-off shaft being rotatably movable about a third axis of rotation that is separate from the first axis of rotation, said third axis of rotation being arranged such that it is not coaxial with said first axis of rotation, and in that in said first drive position of said selective drive member and when said engine rotates said at least one corresponding input wheel, said at least one input wheel rotates said bevel gear pair, said accessory gear and said first driven shaft of said accessory gear box and simultaneously rotates said take-off shaft and said second driven shaft of said accessory gear box. • a first drive position in which one of said engines, of which there is at least one, rotates both said at least one rotor (3, 103, 103') and a first driven shaft of said accessory gear box, and • a second drive position in which one of said engines, of which there is at least one, rotates a second driven shaft of said accessory gear box, said second driven shaft being separate from said first driven shaft, • a bevel gear pair having intersecting axes and, made up of a first bevel gear, referred to as a "power gear", that is provided with teeth and is rotatably movable about a first axis, and of a bevel wheel that is provided with teeth and is rotatably movable about a second axis, said respective teeth and of said first bevel gear and said bevel wheel interacting with one another in a complementary manner, said bevel wheel being arranged to rotate said at least one rotor (3, 103, 103'), • a "take-off" shaft that is constantly rotated by said at least one input wheel, said take-off shaft allowing rotary motion to be constantly transmitted to said second driven shaft of said accessory gear box without rotating said bevel gear pair and the accessory gear, in said second drive position of said selective drive member and when said engine rotates said at least one corresponding input wheel, said input wheel rotates said take-off shaft and said second driven shaft of said accessory gear box,