In the present paper, the authors obtain theoretically the response curves of summed and differential harmonic oscillations induced by symmetrical and unsymmetrical nonlinearities of spring forces, and they investigate the influences of nonlinearities and damping force of those vibrations. Further the stability criteria of vibrations are analytically studied. The conclusions obtained are as follows : (1) The charcteristics of summed and differential harmonic oscillations are analogous to those of subharmonic oscillations in the order of 1/2 and 1/3. (2) There are the critical values of damping coefficients, and summed and differential harmonic oscillations cannot take place, when the magnitudes of damping are larger than these values. (3) The loci of vertical tangent of the response curves divide the response curves into two parts, and the upper parts of the loci constitute a stable range, the lower ones an unstable range.