A detailed analysis is given of the conditions for the generation of misfit-induced defects (misfit wedge disclinations and disclination dipoles, periodical arrays of misfit wedge disclinations, and misfit-dislocation walls (MDWs)) in a two-phase cylindrical composite misfitting system. It is shown that the nucleation of the above defects may be favoured in some range of parameters which include substrate and film thicknesses, misfit eigenstrain, and disclination strength or MDW misorientation angle. The limiting case of massive (cylindrical or planar) substrate is specially investigated. The conditions for the misfit defect formation in cylindrical and planar misfitting composites are compared. The peculiarities of misfit defect generation in cylindrical composite systems are briefly discussed.