The low-frequency perturbations characterized by the inequalities

where X  denotes any component of the plasma-element displacement vector, В is the total magnetic field, ψ is a mark of magnetic surface, and b is the typical scale of variations, equilibrium-value are considered in the magnetospheric plasma. The equations for small oscillations describing both small-scale and large-scale perturbations were obtained from the ideal MHD equations using the common properties of the differential operators in an arbitrary stream-coor­dinate system, the assumption of ballooning for the perturbation components, and the dipole model for the geomagnetic field. It is shown that in the "cold" plasma approximation these equations describe the toroidal and poloidal Alfven modes. It is found that a finite pressure of plasma generates an additional slow magnetosonic oscillation branch which is "coupled" with the poloidal Alfven mode. The stability of ballooning modes is investigated. It is shown that the poloidal Alfven modes become unstable when the pressure increases. The dependence of the stability limit on the plasma pressure and its profile and on the Mcllwain parameter was analyzed by using its energetic principle and the set of small oscillation equations. The results of numerical calculations for the stability limit of ballooning modes for the typical plasma parameters and radial pressure profiles of magnetospheric plasma are presented.