A unit for applying opening devices on packages of pourable food products, comprises a first conveying device to feed the opening devices along a first path, a second conveying device to feed the packages along a second path, a third conveying device movable about a first axis to displace the opening devices along a third path from a withdrawal station to an application station of the opening devices, a gripping member for gripping an opening device, and a supporting plate to support the gripping member; wherein the supporting plate is coupled to the third conveying device; the gripping member is displaceable, at the application station in a defined plane by a first direction transversal to the first axis and to the second path, and by the first axis.