Let G = (V; E) be a finite and simple graph of order n and maximum degree . A signed total strong Roman dominating function on G is a function f : V ! f 1; 1; 2; : : : ; d =2e + 1g satisfying the conditions: (i) for every vertex v of G, Pu2N(v) f (u) 1, where N (v) is the open neighborhood of v, and (ii) every vertex v satisfying f (v) = 1 is adjacent to at least one vertex u such that f (u) 1 + jN (u) \ V 1j =2 , where V 1 = fv 2 V j f (v) = 1g. The signed total strong Roman domination number of G, stsR(G), is the minimum weight of a signed total strong Roman dominating function. In this paper, some bounds for this parameter are presented.