This paper applies survival analysis to ascertain the key empirical determinants of the duration of terrorist hostage-taking incidents during 1978-2018. Our theoretical hypotheses are primarily based on John Cross's bargaining model where negotiation duration depends on initial negotiation spread, bargaining costs, and perceived uncertainty. For hostage events, greater initial demands of the terrorists increase incident length by augmenting the negotiation spread. Sequential release of hostages, demanding the release of imprisoned comrades, changing demands during negotiations, capturing of protected persons, and engaging in kidnappings lengthen hostage incidents by affecting bargaining costs and perceived uncertainty. The number of nonterrorists wounded and the heterogeneity of the hostage-taking squad generally reduce incident length. Based on a competing-risk analysis, we identify factors, consistent with Nash bargaining, affecting three alternative outcomes for hostage incidents.