Abstract: The problem of coupling between the nutational oscillation of a gyro containing three component liquids and the natural oscillation of the rotating liquids themselves is investigated .The interfacial tension is considered in the free surface bounding the liquids. The linearized equations are treated analytically using the Stewartson's and Zhukovsky's theory . The stability of motion is investigated using the method of residues. It is shown theoretically that instability can occur when any of the perio...