A control system for operating two engines (3, 4) is installed on a construction machine, such as a hydraulic shovel, to provide for the operation of either engine or both of the engines, to improve operability and to reduce the stress on the operator. The control system has a governor controller (5, 6) for each engine, a dial potentiometer (1) for providing a throttle signal representing the desired revolution rates of the engines from a low speed to a high speed, and a selector switch (2) having a plurality of control positions (F, N and R) for selecting an individual engine or a combination of the engines. In a first control position (F), the selector switch (2) connects the dial potentiometer (1) to only the governor controller (5) of the first engine (3); in the second control position (N), the selector switch (2) connects the dial potentiometer (1) to the governor controllers (5 and 6) of both engines (3 and 4); and in the third control position (R), the selector switch (2) connects the dial potentiometer (1) to only the governor controller (6) of the second engine (3). The selector switch circuit can employ a relay (Re) to actuate relay switches (Re.sub.1, Re.sub.2) to provide the desired switching.