Distribution functions in hard processes can be described by quark-quark correlators, nonlocal matrix elements of quark fields. Color gauge invariance requires inclusion of appropriate gauge links in these correlators. For transverse momentum dependent distribution functions, in particular important for describing T-odd effects in hard processes, we find that new link structures containing loops can appear in Abelian and non-Abelian theories. In transverse moments, e.g., measured in azimuthal asymmetries, these loops may enhance the contribution of gluonic poles. Some explicit results for the link structure are given in high-energy leptoproduction and hadron-hadron scattering. © 2004 Elsevier B.V.