The linear stability of core-annular flow in rotating pipes is analyzed. Attention is focused on the effects of rotating the pipe and the difference in density of the two fluids. Both axisymmetric and nonaxisymmetric disturbances are considered. Major effects of the viscosity ratio, interfacial tension, radius ratio, and Reynolds number are included. It is found that for two fluids of equal density the rotation of the pipe stabilizes the axisymmetric (n= 0) modes of disturbances and destabilizes the nonaxisymmetric modes. Except for small script R sign, where the axisymmetric capillary instability is dominant, the first azimuthal mode of disturbance |n| = 1 is the most unstable. When the heavier fluid is outside centripetal acceleration of the fluid in the rotating pipe is stabilizing; there exists a critical rotating speed above which the flow is stabilized against capillary instability for certain range of small script R sign. When the lighter fluid is outside the flow is always unstable.