Interdependent values (IDV) is a valuation model allowing bidders in an auction to express their value for the item(s) to sell as a function of the other bidders' information. We investigate the incentive compatibility (IC) of single-item auctions for IDV bidders in dynamic environments. We provide a necessary and sufficient characterization for IC in this setting. We show that if bidders can misreport departure times and private signals, no reasonable auction can be IC. We present a reasonable IC auction for the case where bidders cannot misreport departures.