A study was made of the influence of ion viscosity and ion hea t conductivity on the drift instability of a weakly collisional plasma of finite pressure in a magnetic field. Drift oscillations, whose phase velocities in the direction of the magnetic field are of the order of the ion thermal velocity, were considered. Instability region boundaries and growth rate s were determined. The influence of ion viscosity and heat conductivity leads to a widening of the instability regions. In the stability regions, the given effects result in damping of the oscillations. The corresponding damping rates were determined.