The dynamics of a self-gravitating plasma is studied in order to examine the propagation of hydromagnetic instabilities. This problem leads to the analysis of Jeans’ criterion. It requires modifications due to nonextensive effects and the presence of an external magnetic field, all these in the framework of C. Tsallis’ statistics [J. Stat. Phys. 52, No. 1–2, 479–487 (1988; Zbl 1082.82501)]. The Boltzmann-Gibbs (BG) statistics require a generalization for the statistical description of such systems, this has been done by Tsallis [loc. cit.]. The main difference in the modified results is the appearence of a factor \(q\) \((0<q<1)\), quantifying the degree of nonextensivity of the system. The limit \(q\to 1\) gives the results in BG statistics. For example, the equation of state of an ideal gas is modified by a factor \({2\over 5-3q}\) in the new theory. Further, the dispersion relations are quoted for linear perturbations of ideal plasma in an external magnetic field in order to show possible modifications of Jeans’ criterion depending on the value of \(q\).