Abstract <p>The phenomenon of anti-resonance arises when the frequency of a periodic drive exciting one of the oscillators of a coupled system is systematically varied. This counter-resonance effect, a result of the interference of the drive and the coupling, is examined in non-linear systems in search of anti-resonance response of the driven component at the higher harmonics. It has been shown that contrary to our expectation this interference leaves an imprint of non-linearity in the linear response function. The spectral function of the anti-resonance response at a higher harmonic behaves similarly as that for the lower harmonic. Our perturbative results have been verified by full numerical simulations.</p> Graphic abstract <p>It is possible to manipulate the strength of the time periodic field to obtain a dip or transparency at the response at the second harmonic of the field in a coupled oscillator system.</p>