A power transmission gearbox for rotorcraft for transmitting rotary movement from at least two engine members to a main shaft, wherein the gearbox presents at least two transmission systems for imparting rotary movement to the main shaft, each of the transmission systems including: an inlet shaft designed to be driven in rotation by an engine member; at least two reduction stages presenting different reduction ratios; a first gearwheel connected to the inlet shaft via a declutchable freewheel, the gearwheel meshing with a first toothed wheel secured to an intermediate shaft defining at least a first reduction stage; a second gearwheel connected to the inlet shaft via a simple freewheel, the second gearwheel meshing with a second toothed wheel secured to the intermediate shaft defining the second reduction stage; a main freewheel mounted on the intermediate shaft to rotate a complementary toothed wheel secured to the main shaft; and a clutch mechanism for the declutchable freewheel.