A standard model for radio channel assignment involves a set V of sites, the set {0, 1, 2, } of channels, and a constraint matrix (w(u, v)) specifying minimum channel separations. An assignment f : V → {0, 1, 2, } is feasible if the distance f(u) - f(v) w(u, v) for each pair of sites u and v. The aim is to find the least k such that there is a feasible assignment using only the k channels 0, 1, , k - 1, and to find a corresponding optimal assignment.We consider here a related problem involving also two cycles. There is a given cyclic order τ on the sites, and feasible assignments f must also satisfy f(τv) f(v) for all except one site v. Further, the channels are taken to be evenly spaced around a circle, so that if the k channels 0, 1, , k - 1 are available then the distance between channels i and j is the minimum of i - j and k - i - j . We show how to find a corresponding optimal channel assignment in O( V 3 ) steps.