Flexural instabilities in moving bands under harmonic tension fluctuat
ion are investigated. The discretized equations of flexural motion rep
resent a periodically perturbed linear gyroscopic system. Explicit con
ditions for the onset of instability are established employing the met
hod of averaging. The effects due to damping, mean band speed, and the
band compliance on the band stability are discussed. The present anal
ysis is adequate in the design of moving bands where it is necessary t
o avoid critical speed ranges.