In the thesis, we introduce singularly perturbed systems. Singularly perturbed gain equations their special structure from resence of different time scales. A slow-fast system involve two kinds of dynamical variables, evolving on very different timescales. The Ratio between the fast and slow time scale is measured by small parameter ?. The fitzhugh-Nagumo equation is simplification of the Hodgin-Huxley model for the membrance potential of nerve axon. We investigate the bifurcations of the slow flow depending on the parameter p. The key component of the slow-fast analysis for FitzHugh-Nagumo equatio is the two dimentional fast Subsystem. We show that fast subsystem of FitzHug -Nagumo equations has a double heteroclinic orbit . In the thesis, we study existence of Hopf bifurcatio in the FitzHug –Nagumo equations Also we study the existence of the singular homoclinic orbit in this equation and we compue the value of parameters that, this singular Homoclinic curve terminate.