A firearm adjustable into single-shot, burst and continuous operation modes is described. For operation in one of the non-continuous modes, an indexing device disposed on the rear portion of a first lever in the firearm trigger mechanism is placed into engagement with an advancing mechanism carried by a second lever that selectively actuates the firearm operating rod. The advancing mechanism has a second indexing device engageable with a plate or other transport device slidably mounted on the second lever and engageable with a catch on the operating rod. When the continuous mode is selected, the indexing device on the second lever rests in an idling recess disposed on the rear portion of the first lever forwardly of the indexing device thereon. An improved cartridge magazine and cartridge construction suitable for use in such firearm, together with improved facilities for operating the breech section of such firearm, are also described.