In this paper1 we study the on-line version of maximum-weighted hereditary subgraph problems. In our on-line model, the final instance (a graph with n vertices) is revealed in t clusters, 2 ? t ? n . We first focus on an on-line version of the maximumweighted hereditary subgraph problem. Then, we deal with the particular case of the independent set problem. We are interested in two types of results: the competitive ratio guaranteed by the on-line algorithm and hardness results that account for the difficulty of the problems and for the quality of algorithms developed to solve them.