An arrangement in liquid pumps, especially petrol pumps, comprising a valve system with the functions of a non-return valve, a pressure relief valve and a ventilating valve, is connected in the delivery line between a liquid pump and a petrol delivery nozzle. The valve system includes a piston and cylinder assembly (18, 19) whose cylinder (18) has an open end communicating with the delivery line (17) and whose piston (19), adapted to move back and forth through the open cylinder end, has a tapered end portion (20, 21). This portion is facing the upstream side of the delivery line passage, and the piston is biased so as to occupy a position in which the tapered piston end portion, with a cross-sectional area thereof which is smaller than its largest cross-sectional area, closes said upstream side by engaging a seat (9′). The taper of the end portion is such that in said position, said largest cross-sectional area is spaced from the seat, as seen in the direction of movement of the piston.