The analysis of the internal structure of concepts reveals the presence of a substantial amount of contextual information. Even though this interaction is easily recognizable, it is not clear how contextual information is processed and included into concept representations. The aim of this paper is to shed light on this question by analyzing the effect that an increasing amount of context exerts on conceptual processing. We report a self-paced reading experiment and a visual world experiment to test two hypotheses about the integration of context information: the incremental activation hypothesis suggests that the degree of facilitation in concept processing increases with the amount of context available; and the immediate activation hypothesis states that once a sufficient amount of contextual support is reached, no more facilitation occurs. Our data are compatible with the latter account.