We consider the role of local orientational mobility for the NMR relaxation of hyperbranched macromolecules modeled in form of Vicsek fractals. The spectral density J(ω), that is relevant for the NMR relaxation, is studied for labeled segments of flexible and semiflexible Vicsek fractals. We show that the semiflexibility leads to strong effects. For flexible Vicsek fractals the function ωJ(ω) has