Micro-instabilities due to resonant interaction between waves and fast ions in an inhomogeneous high pressure plasma in a magnetic field with constant curvature are investigated. The influence of the magnetic field curvature and the fast-ion pressure on the resonance conditions and growth rate of the Alven-type long wavelength drift oscillations are studied for a broad range of parameters. The general expressions obtained are used to investigate the excitation of Alfven waves by fast ions with (a) Maxwellian and (b) 'loss cone' velocity distributions.