This paper introduces an extension of the Steiner tree problem applied to dynamic graphs. In various application domains of this problem, the associated graphs undergo temporal changes, such as variations in the edge set or associated costs. The paper presents three extension models, and we opt for the one demonstrating the most desirable features: a fixed Steiner set (a set of selected vertices) maintained throughout the time horizon and of minimum cardinality, ensuring connectivity among the terminal vertices. We show that the resulting problem of minimizing the size of the Steiner set is NP-hard, even when dealing with only two terminals and a lifetime of 2 time steps. This contrasts with the corresponding static problem, which is among the rare polynomial versions of the Steiner tree problem. However, polynomial algorithms exist when the size of the Steiner set is bounded. An algorithm is designed, analyzed and tested on specially generated and on real data sets. We show that it solves exactly non trivial instances when the Steiner set size in bounded.