Abstract In this paper we present a new kind of dynamic assignment model for public transport, including transit and pedestrian networks, that is capable of representing single runs, whose schedule is possibly affected by congestion. To this end we avoid introducing explicitly a diachronic graph and rely just on a spatial/functional graph, like in frequency based models. More specifically, we here extend to transit networks the framework of the Link Transmission Models, so far applied only to road networks (Yperman, 2007; Gentile, 2010; Gentile, 2015). The focus of LTM is the propagation, affected by congestion, of flows on the network, for given route choices. In this framework, both schedule based and frequency based passenger behaviors can be implicitly simulated by properly setting time-varying splitting rates. The core of the proposed Transit Link Transmission Model (TLTM) is the node model, which aims at reproducing the flow conflicts (congestion) occurring at bus stops and rail platforms, such as: passengers that fail-to-board or fail-to-sit due to vehicle overcrowding, vehicles queueing to serve a stop, doors opened longer to allow passengers alighting and boarding. The formulation and implementation of the TLTM will be presented in the following, while the application of the model on test and real networks will be presented in a forthcoming paper.