An engine unit for an aircraft including a turboprop engine and its device for mounting on to a wing surface. The device includes a rigid structure and a mechanism for fastening the turboprop engine on to this structure. The fastening mechanism includes six mutually independent hydraulic systems, each one exclusively dedicated to the transfer, to the rigid structure, of forces exerted respectively according to one of the six degrees of freedom of movement. Each hydraulic system includes at least one hydraulic jack with a piston attached to one of the two elements, i.e. either the turboprop engine or the rigid structure, together with a cylinder housing the piston and attached to the other of the two elements.