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Abstract. The sufficient condition for the existence of 2π-periodic solutions of the following third-order functional differential equations with variable coefficients a(t)x^m(t)+bx^2k-1(t)+cx^12k-1(t)+∑↑2k-1i=1cix^i(t)+g(x(t-τ))=p(t)=p(t+2π)is obtained.