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The sufficient condition for the existence of 2π-periodic solutions of the following third-order functional differential equations with variable coefficientsa(t)x(t)+bx″2k-1(t)+cx′2k-1(t)+2k-1i=1cixi(t)+g(x(t-τ))=p(t)=p(t+2π)is obtained. The approach is based on the abstract continuation theorem from Mawhin and the a-priori estimate of periodic solutions.