The evolution in time of the g×B instability in a collisionless finite Larmor radius plasma is considered in the flute approximation. The gravity constant g is increased above its neutral stable value such that there is only one slightly unstable mode according to linear theory. Hence, two times scales are present, and the multiple time scale method can be applied. As a result, a modulation in the amplitude of the unstable mode is obtained which for small dissipation gives limit cycle behavior. The steady-state oscillation is found to be stable.