An asteroidal triple is a stable set of three vertices such that each pair is connected by a path avoiding the neighbourhood of the third vertex. Let G be a graph with vertex set V (G) and edge set E(G), the total graph T(G) of G has vertex set V (G)∪E(G) and two vertices in T(G) are adjacent if and only if they are adjacent or incident in G. In this paper, we try to characterize the total graph of interval graphs and proper interval graphs.