Let k be a positive integer. A k-circular-L(2, 1)-labelling of a graph G is an assignment f from V(G) to {0, 1, horizontal ellipsis , k-1} such that, for any two vertices u and v, |f(u) - f(v)|(k) >= 2 if u and v are adjacent, and |f(u) - f(v)|(k) >= 1 if u and v are at distance 2, where |x|(k) = mi