A power plant (1) having two engine groups (10, 20) and a main gearbox (MGB) (2), and a rotary wing aircraft (30) having such a power plant (1). Each engine group (10, 20) drives said MGB (2) mechanically to rotate a main outlet shaft (3) and, consequently, a main rotor (31) of said aircraft (30) at a frequency of rotation NR. A first engine group (10) has two main engines (11, 12) and is by a first setpoint NR* for said frequency of rotation NR, while a second engine group (20) has one secondary engine (21) and is regulated by a second setpoint W1* for power from said second engine group (20). The first engine group (10) is also regulated by a third setpoint W2f* for anticipating power such that said first engine group (10) and said second engine group (20) deliver the power needed at said main rotor (31).