In this paper we develop a stochastic, dynamic network equilibrium model of airline passenger transportation. The model explicitly incorporates the behavior of the passengers in regard to the decision whether to travel or not, and route selection, and formalizes the passenger's decision process as an abstract network. The equilibrium between the realized demand for the routes of travel and the supply of the seats is shown to satisfy a system of nonlinear equations. A Gauss-Seidel algorithm is then proposed for the computation of the equilibrium and conditions for convergence established. Finally, the algorithm is applied for the computation of the Air Canada airline passenger network equilibrium problem.