A nonlinear kinetic-fluid model for high &bgr; plasmas with multiple ion species which can be applied to multiscale phenomena is presented. The model embeds important kinetic effects due to finite ion Larmor radius (FLR), wave-particle resonances, magnetic particle trapping, etc., in the framework of simple fluid descriptions. When further restricted to low-frequency phenomena, with frequencies less than the ion cyclotron frequency, the kinetic-fluid model takes a simpler form in which the fluid equations of multiple ion species collapse into one-fluid density and momentum equations and a low-frequency generalized Ohm's law. The kinetic effects are introduced via plasma pressure tensors for ions and electrons which are computed from particle distribution functions that are governed by the Vlasov equation or simplified plasma dynamics equations such as the gyrokinetic equation. The ion FLR effects provide a finite parallel electric field, a perpendicular velocity that modifies the E¿B drift, and a gyroviscosity tensor, all of which are neglected in the usual one-fluid MHD description. Eigenmode equations are derived, which include magnetosphere-ionosphere coupling effects for low-frequency waves (e.g., kinetic/inertial Alfv¿n waves and ballooning-mirror instabilities). ¿ 1999 American Geophysical Union