Abstract: In this paper, first we study normal form theory with Z2-symmetry and universal unfolding theory of the degenerate vector field. Then we use above mentioned theory to study degenerate bifurcations of codimension two in nonlinear oscillator under combined parame-tric and forcing excitation. Thereby stability problems with double zero eigenvalues can be solved. Finally the curves for homoclinic bifurcaron in parameter plane are given by using Melnikov's method and the existence of global bifurcation is discus...