Abstract: An incidence geometry consists on a set of points X of points and a set of blocks, or lines (subsets of X), such that two blocks intesect in at most one point. An incidence geometry is a *configuration* if every line has the same number of points and every point is incident with the same number of lines. A configuration is *cyclic* if its automorphism group contains a regular cyclic subgroup. The isomorphism problem for cyclic configurations asks for sufficient conditions to check wether two cyclic configurations are isomorphic or not. We say that two cyclic configurations are *multiplier equivalent* if some element of the multiplicative group of Z_n induces an isomorphism. A related problem is that for which n two isomorphic cyclic configurations  are multiplier equivalent. In this talk we show some known results for general cyclic combinatorial objects and we present some partial results for the latter problem.