[en] A collisionless two-fluid theory based on a fourteen-moment generalization of the 'double-adiabatic' equations is developed to lowest order in the Larmor radius parameter, and applied to derive the toroidal η_i stability boundary for all values of the ratio of the density gradient scale length divided by the field curvature length. The present model is an improvement over existing collisional two-fluid models in view of the collisionless nature of the η_i instability, while retaining the advantage over kinetic theory of the practability of mode-coupling simulations. The linear stability boundary, linear growth rate and real frequency agree fairly accurately with draft-kinetic theory