Abstract  In this paper we study the homotopy type of Hom(C_m,C_n), where C_k is the cyclic graph with k vertices. We enumerate connected components of Hom(C_m,C_n) and show that each such component is either homeomorphic to a point or homotopy equivalent to S¹. Moreover, we prove that Hom(C_m,L_n) is either empty or is homotopy equivalent to the union of two points, where L_n is an n-string, i.e., a tree with n vertices and no branching points.