Two models of gamma-ray bursts using the theory of byuons (TB) are considered. This theory describes a “life’ of special unobservable discrete objects from which the surrounding space and the world of ultimate particles are formed. Basic axioms and some conclusions of this theory are discussed. The results of experimental investigations of new non-gauge interaction (using high current magnets, torsion and piezo resonance balances, and changes in the rate of β - decay of radioactive elements etc.) are described. It is shown that basic problems with nature of gamma-ray bursts can be solved in the framework of this theory not only for bursts connected with supernova explosions but also for those without explosions. The conditions for ejection of matter during a SN explosion due to the non-gauge force action are shown.