This paper studied the characteristics of stochastic resonance in the neighborhood of bifurcation point of two nonlinear dynamic systems, the pitchfork bifurcation system and FitzHughNagumo (FHN) cell model. The results of research show t hat the two nonlinear dynamic systems have the same bifurcation characteristic o f transition from one to two attractors (or from two to one attractors) when the bifurcation of each system occurs, that is, in the neighborhood of the bifurcat ion point there exist attractors before and after bifurcation on the both sides of the bifurcation point. Under the perturbation of noise, a transition may occu r between the two coexisting attractors on the right side of the bifurcation poi nt, in a way like the mechanism of traditional stochastic resonance; moreover,an other transition may also occur among the three attractors (one before bifurcati on and two after it) on two sides of the bifurcation point, which can induce sto chastic resonance alone. When the two types of transitions occur, the stochastic resonance induced by the second type of transition continues in a wide intensit y range of noise, which causes the first type of transition; and the stochastic resonance induced by the first type of transition stops in a rather small range of the noise intensity,and then causes the second type of transition.