A control system is provided for a combine or other vehicle having an engine (30) for driving both the ground wheels (40) of the vehicle and at least one auxiliary mechanism (42), such as the crop-processing mechanisms of a combine. The engine is coupled to the ground wheels through a hydrostatic transmission (41) and the power takeoff (43) for the auxiliary mechanism is located on the engine side of the transmission. A speed droop governor (31) regulates the fuel input to the engine in response to changes in the engine speed. Transmission control means (44, 46, 45) adjusts the setting of the hydrostatic transmission, and thus the load applied to the engine via the transmission, in , response to changes in engine speed or another parameter that varies with engine load so as to control the speed changes effected by the droop governor. The combined effect of the speed droop governor and the transmission control means is to gradually reduce the operating speed of the engine as the fuel input to the engine is increased, with the total speed reduction over the full load range of the engine comprising from about 1% to about 5% of the no-load speed.