Let G = (V, E) be a simple graph with no isolated vertices and p ≥ 3. A set D ⊆ V is a dominating set, abbreviated as DS, of a graph G, if every vertex in V −D is adjacent to some vertex in D, while a total dominating set, abbreviated as T DS, of G is a set T ⊆ V such that every vertex in G is adjacent to a vertices in T . A set T is a superlative total dominating set, abbreviated as ST DS, of G if V − T is not contains a T DS but it contains a DS of G. The superlative total domination number γst(G) is the minimum cardinality of a ST DS of G. In this paper, we initiate a study on γst(G) and its exact values for some classes of graphs. Furthermore, bounds in terms of order, size, degree and other domination related parameters are investigated.