This paper proposes a formulation of deterministic equilibrium in a public transit corridor that takes into account the congestion effect as perceived directly in travel times. The identification of the relationship between flows and travel times includes time at transit stops for passenger boarding and alighting. A simple case is analyzed that demonstrates the existence of equilibria in which identical users adopt different travel strategies, and a method is supplied for determining such an equilibrium. To find the general case assignment for a corridor, an assignment algorithm based on incremental flow increases is also presented. Finally, the algorithm is implemented in a simple corridor. The results show that identical users faced with the same trip must be allowed to take different decisions for an equilibrium assignment to exist.