Cyclic $(n,m)$-groopoids which represent a generalization of cyclic $n$-ary quasigroups and semisymmetric quasigroups are defined and considered. If S is a nonempty set, $m,n$ positive integers and $F$ a mapping of $S^n$ into $S_m$ such that for all $x_1,\dots,x_{n+m}\in S$ $F(x_1,x_n)=(x_{n+1},\dots,x_{n+m}$ implies $F(x_2,\dots,x_{n+1})=(x_{n+2},\dots,x_{n+m},x_1$ then $(S,F)$ is called a cyclic $(n,m)$-groupoid. Some properties of such $(n,m)$-groupoids are determined and it is proved that every cyclic $(n,m)$-groupoid can be generated by an $n$-ary groupoid satisfying an identity.