The paper illustrates the preliminary activity of an extensive research program oriented to investigate the multiaxial fatigue behaviour of unidirectional composite laminates, with particular attention to the analysis of the damage mechanisms and their correlation with the local multiaxial stress state to be used then as the basis for the development of multiaxial fatigue criterion. The definition of an effective experimental procedure for multiaxial fatigue testing is carefully discussed in terms of specimen geometry, specimen manufacturing and local stress state. Once identified in the thin-walled tubular specimens under tension–torsion loading the best test configuration for the aims of the research, the results of comparative fatigue tests investigating the influence of the tubes geometry (wall thickness to diameter ratio) on the transverse fatigue response are presented. In the final part of the paper the effects of an increasing shear stress component (σ6) on the transverse (σ2) fatigue strength and damage evolution in UD glass–epoxy tubes are illustrated.