The particle dynamics and in the stellar magnetosphere during gravitational collapse is investigated. The formations of relativistic jets and the generation of the radiation bursts in the stellar magnetosphere by gravitational collapse are considered. As follows from results, the stars on the stage of gravitational collapse must be powerful sources of the relativistic jets and the non-thermal radiation. These jets will formed in the polar caps of collapsing stars magnetospheres, when the stellar magnetic field increases during collapse and the charged particles will be accelerate. These jets will generate the non-thermal radiation. The radiation flux grows with decreasing stellar radius and can be observed in the form of radiation burst in wide band wave- from radio to gamma-ray. These bursts radiation can be observed as gamma- and X- rays bursts.