We report an experiment in which subjects named 120 pictures, consisting of series of five pictures drawn from each of 24 semantic categories (and intermixed with 45 fillers). The number of intervening trials (lag) between successive presentations of members of the same category varied from two to eight. Subjects' naming latencies were slowed by 30 ms for each preceding member of the category. This effect was both cumulative and linear, and unrelated to the lag elapsing since the previous presentation of a category member. These results definitively demonstrate the occurrence of cumulative interference for word retrieval by prior retrieval of other exemplars of the same semantic category—cumulative semantic inhibition. We claim that this inhibition effect could only occur if the spoken word production system possesses three specific properties (competition, priming, and sharing of semantic activation). We provide computational-modelling evidence in support of this claim. We show that no current theory of spoken word production has all of these properties. In their current form, all these theories are falsified by these results. We briefly discuss the obstacles that may be encountered by current models were they modified to account for our findings.