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We study adaptive route hoi e models that expli itly apture travelers' route hoi e adjustments a ording to information on realized network onditions in sto hasti time-dependent networks. Two types of adaptive route hoi e models are explored: an adaptive path model where a sequen e of path hoi e models are applied at intermediate de ision nodes; and a routing poli y hoi e model where the alternatives orrespond to routing poli ies rather than paths at the origin. A routing poli y in this paper is a de ision rule that maps from all possible (node, time) pairs to next links out of the node. A poli y-size Logit model is proposed for the routing poli y hoi e, where poli ysize is a generalization of path-size in path hoi e models to take into a ount the overlapping of routing poli ies. The spe i ations of estimating the two adaptive route hoi e models are established and the feasibility of estimation from path observations is demonstrated on an illustrative network. Predi tion results from three models non-adaptive path model, adaptive path model, and routing poli y model are ompared. The routing poli y model is shown to better apture the option value of diversion than the adaptive path model. The di eren e between the two adaptive models and the non-adaptive model is larger in terms of expe ted travel time, if the network is more sto hasti , indi ating that the bene t of being adaptive is more signi ant in a more sto hasti network.