Using the anal.vtical and numerical approaches, the nonlinear dynamic behaviors in the vicinity of several compound critical points are studied for a simply supported functionally graded materials(FGMs) rectangular plate subjected to the transversal and in-plane excitations in a thermal environment.The resonance case considered here is 1:1 internal resonance and primary parametric resonance.Three.types of critical points are considered, which are characterized by a double zero eigenvalue, a simple zero and a pair of pure imaginary eigenvalues, and two pairs of pure imaginary eigenvalues, respectively.