As shown recently by Y. Osaki super-massive stars with mass M < 3.5 × 105M⊙ can, in the absence of rotation, reach the hydrogen-burning main sequence before the onset of general relativistic instability. Such objects are then pulsationally unstable. A considerable simplification is introduced if one considers only very massive stars, for which the relative amplitude of the fundamental mode of oscillation is practically constant. This sets a lower limit of 104M⊙ to the mass that can be considered. The upper limit is also reduced to 2 × 105M⊙ if one neglects the relativistic correction. One necessary step in the study of non-linear oscillations of massive stars is to derive a differential equation for the adiabatic pulsations. The relativistic correction could be taken into account in the following way.