Let j, k and m be three positive integers, a circular m-L（j, k）-labeling of a graph G is a mapping f： V（G）→{0, 1, …, m-1}such that f（u）-f（v）m≥j if u and v are adjacent, and f（u）-f（v）m≥k if u and v are at distance two,where a-bm=min{a-b,m-a-b}. The minimum m such that there exists a circular m-L（j, k）-labeling of G is called the circular L（j, k）-labeling number of G and is denoted by σj, k（G）. For any two positive integers j and k with j≤k,the circular L（j, k）-labeling numbers of trees, the Cartesian product and the direct product of two complete graphs are determined.
