Consider the effect of nonlinear spring and linear viscous damping in structure, the motion equations of a helicopter blade-absorber system has been established by Lagrange equation. Since the helicopter blade-absorber system exists motion coupling, the inertia and stiffness terms of equations are decoupled via equivalent principal coordinate transformation. The stability and local bifurcation behaviors of the principal coordinate equations are investigated with the aid of multiple scales method and normal form theory. Two kinds of critical points for the bifurcation response equations near the combination resonance are considered, which are characterized by a pair of purely imaginary eigenvalues and double zero eigenvalues. The Hopf bifurcation solution, bifurcation path, and transition curves of the model are investigated respectively. For each case, the numerical results obtained by Runge-Kutta method coincide with the analytical predictions. These results may provide some guidance for parameter design of helicopter blade-absorber system
