Let ℤn  be the set of integer modulo n. The Cayley graph on ℤn is an undirected graph whose vertex set is ℤn and two vertices a, b are adjacent if and only if a – b ϵ S ⸦  ℤn\{0}. The addition Cayley graph on ℤn  is a graph whose vertex set is ℤn  and two vertices a, b are adjacent if and only if a + b ϵ A ⸦ ℤn.  In this paper , we characterize Cayley graphs and addition Cayley graphs of even orders. Their basic properties of them are investigated. We also give exact values for the total chromatic numbers of Cayley graphs and addition Cayley graphs where their orders are even integers. Moreover, we provide examples to illustrate these results.