The purpose of the article is to present new solutions of the Mathieu Duffing equation in the zone of the principal parametric resonance – the stationary solutions with the frequency equal to the frequency of parametric excitation. These solutions are obtained by combining numerical and analytical research methods, but their verification is done by direct integration of the original equation. Initially monoharmonic analysis of the solutions under study has been performed, and this analysis gave contradictory and inconsistent results. Only further polyharmonic approach has made it possible to do definite conclusions