[en] Annihilation effect on positions and widths of the quasinuclear s-wave resonances in the NN system is investigated in the framework of the simple two-channel potential model. The equation is obtained that determines the shift of the quasinuclear levels depending on the channel coupling constant lambda. It is shown that under certain conditions an appearance of the annihilation results in a decrease of the total resonance width. The physical reason of this phenomenon is discussed. Dependence of partial widths of the quasinuclear resonances on the constant lambda is found. It is shown that at lambda→ infinity the annihilation width GITAsub(an)→0. It is shown that small shifts of the quasinuclear levels are compatible with the large annihilation cross section observed experimentally