A?composite?laminated?thin?plate?was?studied?for?analyzing?the?dynamic?behavior?near?a?critical?point?characterized?by?initial?resonance.?Based?on?the?averaged?equations,?the?transition?boundaries?were?sought?to?divide?the?parameter?space?into?a?set?of?regions,?which?correspond?to?different?types?of?solutions.?The?Hopf?bifurcation?theorem?was?used?to?investigate?the?stable?conditions?of?respective?equilibrium?points.?Then,?the?conditions?of?the?occurrence?of?double?Hopf?bifurcations?were?found,?and?two?types?of?periodic?solutions?may?bifurcate?from?the?initial?equilibrium.?Based?on?bifurcation?theory,?it?is?shown?that?the?composite?laminated?thin?plates?exhibit?different?periodic?motions.