1. Double firing mode semi-automatic handgun, comprising a frame (1), a barrel (2), a spring biased slide (3), a trigger (4) and a firing assembly with a firing rod (14) operated by the trigger (4), comprising a frame pocket (11) provided in a rear part of the frame (1) and being open from above, in which in hammer mode an associated frame inset (5) and in striker mode an associated other frame inset (7) can be inserted, and the rear part of the slide (3) comprises a slide pocket (12) in which in hammer mode an associated slide inset (6) and in striker mode an associated other slide inset (8) can be inserted, and in front of the connection site of the slide pocket (12) and behind the barrel (2) a firing pin (9) is arranged extending to a cartridge receiving chamber (21), and in both firing modes the frame insets (5 or 7) and the slide insets (6 or 8) cooperate and by means of the rearward motion of the firing rod (14) a surface is pushed on the frame inset (5 or 7), namely in hammer mode a surface of a releasing bolt (55) and in striker mode a buffer face (75), and this pushing movement is transformed into an axial hit on the firing pin (9) by a spring bias or by the release of a lock.