A straight travelling apparatus for heavy construction equipment such as excavator or crane, including a straight travel valve disposed in both lines respectively branching from first and second hydraulic pumps and switched between a first state at which a fluid delivered from the first hydraulic pump is supplied to a right travel motor and a part of the actuators of a working system while a fluid delivered from second hydraulic pump is supplied to a left travel motor and the remaining part of the actuators of the working system and a second state at which the fluid delivered from the first hydraulic pump is supplied to both the right and left travel motors while the fluid delivered from the second hydraulic pump is supplied to all actuators of the working system, first and second pilot fluid lines both branching from the pilot pump, a connecting fluid line adapted to communicate the first and second pilot fluid lines with each other, a fluid line branching from the connecting fluid line, and a relief check valve disposed at a predetermined position between a branching point where the fluid line branches from the connecting fluid line and a connecting point where the connecting fluid line is connected to the second pilot fluid line.