For positive number d, an L(1, d) -labeling f of G is an assignment of numbers to vertices of G such that |f(u) - f(v)| ≥ 1 if d(u, v) = 1, and |f(u) - f(v)| ≥ d if d(u, v) = 2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(1, d) -labeling number of G, denoted by λ1,d (G), is the minimum span over all L(1, d) -labelings of G. In this paper, the authors give the L(1, d) -labeling numbers of the direct product of two cycles Cm and Cn for d ≥ 2 for some values of m and n. Some cases for 1 ≤ d