Nonaxisymmetric bifurcation behaviours of composite tubes two different materials subjected to uniform radial shrinkage at the external surface have been investigated and compared with those of single tube. The effect of material parameters normalized with respect to those of outer tube upon the bifurcation point and corresponding mode has been clarified. The parameters substantially affect the bifurcation mode with long-wavelength so that the composite tube with low hardening exponent or with high yield stress of inner tube destabilizes the overall deformation of the tube. However surface type bifurcation, short-wavelength mode, shown on the traction-free inner surface is hardly affected by the material parameters. The surface type bifurcation completely depends on the material characteristics of inner tube and the bifurcation point of composite tube almost coincides with the of single tube.