Abstract: A 1∶3 resonant double Hopf bifurcation occurring in a limit cycle oscillator under time delayed linear and nonlinear feedbacks was studied. By using the method of multiple scales, the complex amplitude equations of 1∶3 resonance were obtained. By letting the complex amplitudes as a mixed polar Cartesian form, the complex amplitude equations were reduced to a three dimensional real amplitude equations. Then the dynamics around the 1∶3 resonant double Hopf bifurcation point was classified in two cases separately. Comparing the two classifications, it was found that there are completely different dynamics in two cases.