In this paper, we consider the asymptotic properties of the numbers of spanning trees and Eulerian trials in circulant digraphs and graphs. Let C(p, s1, s2, . . . , sk) be a directed or undirected circulant graph. Let T (C(p, s1, s2, . . . , sk)) and E(C(p, s1, s2, . . . , sk)) be the numbers ∗This work was partially supported by the Natural Science Foundation of China, email: fjzhang@jingxian....