A displacement-controlled hydraulic system for installation on a multi-function machine, and multi-function machines equipped with the hydraulic system and having devices for propelling the machine, at least a first implement, and multiple actuators that perform multiple functions of the machine. The multiple actuators include first actuators that control the first implement and second actuators that control the propelling devices. The hydraulic system comprises multiple pumps for controlling the first actuators and optionally the second actuators, and valves that enable at least one of the pumps to sequentially control two of the multiple actuators and a corresponding two functions of the multiple functions performed thereby. None of the pumps sequentially controls the second actuators in combination with any of the first actuators.