Riveting apparatus of the type in which an elongated mandrel (30), having an enlarged head at one end and loaded with a plurality of the tubular rivets (40) forming a column of rivets on the mandrel, is gripped by gripping means (43) at or near the end remote from the head, and reciprocated relative to an abutment (32) by relative reciprocation between the gripping means (43) and the abutment (32), the rivets (40) in the column being fed forwardly along the mandrel (30) so that the leading rivet nearest the mandrel head is positioned between the mandrel head and the abutment (32) and can then be set by moving the mandrel (30) rearwardly relative to the abutment (32) so as to draw the head of the mandrel through the bore of the rivet (40) while the rivet is supported by the abutment (32), includes pneumatically operated rivet-feeding means (55) for feeding rivets (40) forwardly along the mandrel (30), and valve means (P.1.2.) for shutting off the supply of air to the rivet feeding means (55) thereby to disable it, and the valve means (P.1.2.) is responsive to the presence or absence of a mandrel (30) in the gripping means (43), the valve means (P.1.2.) being closed in the absence of a mandrel (30) and open only in the presence of a mandrel (30).