How should inventory management respond when there is a possibility of imminent obsolescence (or, more generally, deteriorating demand)? We use an inventory-control model to address this question. The model incorporates a Markovian submodel to describe the uncertain events leading to obsolescence. These events and their uncertainties come in a variety of patterns. We devote considerable attention to specifying the submodel, and we compare a few alternatives numerically. Also, we compare optimal policies to simpler alternatives, and we investigate the response of the model to parameter changes. Generally, we find that obsolescence does (or should) have a substantial impact in the way inventories are managed. The nature of these effects, moreover, is fairly intricate. It appears that obsolescence cannot be captured in a simpler model through parameter adjustments. These conclusions presume that we cannot dispose of excess stock, either directly or through price promotions; we show also that the disposal option can make the problems of obsolescence more manageable. © 1996 INFORMS.