The present paper is concerned with the response of two internal resonant oscillators subjected to combined quadratic parametric excitation and external excitation with the same frequency. Two-to-one and one-to-two internal resonances are presented. Using multiple scales method, four first-order ordinary differential equations are derived to describe the modulation of the amplitudes and the phases, when principal parametric resonances of the second mode and combination parametric resonances of the additive type occur. In all cases the steady state solutions and their st ability are determined. Numerical results depicting various resonances are presented.