The adaptive multimodal least expected time (AMLET) algorithm is presented for determining the adaptive least expected time (LET) hyperpaths from all origins to a specified destination for all departure times in a period of interest in stochastic, time-varying multimodal networks, when the "fastest" path can be appropriately selected depending on the arrival time at each node en route. Mode transfer delays are incorporated into the algorithm to represent waiting times required in transferring modes, such as between driving and boarding a transit vehicle. Both mode transfer delays and arc travel times may be stochastic and time varying. By considering stochastic, time-varying networks, the proposed algorithm can more realistically represent conditions in transportation networks than can exist in deterministic approaches. The resulting solutions provide not only the adaptive LET hyperpaths but also the travel mode to choose from along each path segment for completing a trip. Travelers are not restricted to traveling on only one path and one mode found to be best before they depart from the origin. Instead, they can choose their paths and travel modes en route in accordance to the knowledge of their arrival time at intermediate nodes. Hence, the solution is a set of hyperpaths instead of a single path to the destination. The AMLET algorithm is tested on a real-world transportation network, with several possible traffic scenarios to illustrate the nature of the solution paths.