This paper deals with the so-called “subjective temporal” use of the conditional tense (Il savait que je viendrais / He knew that I would come). First we will expose the difficulties to which is confronted the analysis of this use by means of the concept of “prospective possibility” (see Gosselin 1999, and in the framework of branching time semantics, Martin 1981, Vuillaume 2001 and Bres 2009). We then propose, in this framework, a new analysis of prospective possibility, which responds to the indicated difficulties and provides new predictions on the semantics of statements using “subjective temporal” conditional tense.