Abstract: The paper is devoted to the study of excess life in renewal process. It is proved in the paper that the excess life γ(t) and γ(t+s) at time t and t+s respectively are asymptotically independent. And it is also shown that the mixed moment Eγ^m(t) γⁿ(t+s) equals asymptotically to the product of the limits lim_t→∞ Eγ^m(t) and lim_t→∞ Eγⁿ(s).