The quotients Gk/Gk+1 of the lower central series of a finitely presented group G are an important invariant of this group. In this work we investigate the ranks of these quotients in the case of a certain class of conjugation-free groups, which are groups generated by x1, . . . , xn and having only cyclic relations: xitxit−1 · . . . · xi1 = xit−1 · . . . · xi1xit = · · · = xi1xit · . . . · xi2...