This paper presents a first approach to dynamic frequency-based transit assignment. As such the model aims to close the gap between schedule-based and frequency-based models. Frequency-based approaches have some advantages compared to schedule-based models, however, when modelling highly congested networks a static frequency-based approach is not sufficient as it does not reveal the peaked nature of the capacity problem. The central idea for dealing with the line capacity constraints is the introduction of a "fail-to-board" probability as in some circumstances passengers are not able to board the first service arriving due to overcrowding. The common line problem is taken into account and the search for the shortest hyperpath is influenced by the fail-to-board probability. An assumption that passengers mingle on the platform allows a Markov network loading process which respects the priority of on-board passengers with respect to those wishing to board. The study period is divided into several time intervals and those passengers who failed to board are added to the demand in the subsequent time interval and so might reconsider their route choice. Trips that are longer than one interval are also carried over to subsequent time intervals. The approach is first illustrated with a small example network and then with a case study relating to London, where transit capacity problems are experienced daily during the peak period. (C) 2008 Elsevier Ltd. All rights reserved.