Abstract: In this paper, we consider the unboundedness of solutions for the asymmetric equation x^’’+ax⁺-bx^-+（x）ψ（x^’）+f（x）+g（x’）=p（t）,where x⁺= max{x, 0}, x^-= max{-x, 0}, a and b are two different positive constants,f（x） is locally Lipschitz continuous and bounded, （x）, ψ（x）, g（x） and p（t） are continuous functions, p（t） is a 2π-periodic function. We discuss the existence of unbounded solutions under two classes of conditions: the resonance case 1/a^1/2+1/b^1/2∈Q and the nonresonance case 1/a^1/2+1/b^1/2∈Q 

Key words: unboundedness, resonance, nonresonance