This paper investigates the dispersion relations of axisymmetric wave propagation in initially twisted bi-material compound cylinders, within the scope of the piecewise homogeneous body model, utilizing 3D linearized wave propagation theory in an initially stressed body. It is assumed that the constituents of the compound cylinder are isotropic and homogeneous. The corresponding eigen-value problem is formulated and the solution method for this problem as well as the algorithm for obtaining the numerical results is developed. The numerical results illustrate the influence of the initial twisting of the compound cylinder on the dispersion of the axisymmetric wave propagation as presented and discussed in the present paper. In particular, it is established that as a result of the existence of the initial twisting, at least in one constituent of the considered compound cylinder, the axisymmetric longitudinal and torsional waves cannot propagate separately, i.e. the new type axisymmetric waves, which differ from the axisymmetric torsional and longitudinal waves, must appear. (C) 2010 Elsevier Ltd. All rights reserved.