In the present work, the stability conditions of the response torque of the system influenced by two-parametric random excitation are investigated when the frequency of the harmonic excitation is in the range of the parametric fundamental resonance. The stability conditions for the first and the second response torque that apply to the first approximation are reached. It is established that the stability conditions depend on the spectral values of the random excitations of zero and double the natural frequency of the oscillator.