We investigate the conditions under which a self-gravitating system of particles of different masses may be gravitationally unstable if there is a systematic correlation between the random velocity of a particle and its mass. For an isotropic uniform medium without rotation but with mass spectrum and velocity depending on the particle mass, a situation arises where the Jeans length for such a system may be significantly smaller than for the case when some mean values are used instead of mass and velocity spectra. For a differentially rotating medium, representing a spiral galaxy, we obtain the analogue of the Toomre parameter for a heterogeneous (multi-component) system. We demonstrate that the gas system in spirals represented by an ensemble of giant molecular clouds may be considerably less stable in the case of random velocity-mass correlation than for a system with unique velocity dispersion.