The topological complexity of a space has been introduced by M. Farber in order to give a measure of the complexity of the motion planning problem in robotics. This invariant is, by its definition, closely related to the Lusternik-Schnirelmann category. By analogy to the notion of weak (LS) category, we define the "weak topological complexity". This invariant is a new lower bound for the topological complexity and turns out to be equal to the weak category of the homotopy cofibre of the diagonal map.  This is joint work with J.M. García Calcines.