Conventional economic wisdom suggests that congestion pricing would be an appropriate response to cope with the growing congestion levels currently experienced at many airports. Several characteristics of aviation markets, however, may make naive congestion prices equal to the value of marginal travel delays a non-optimal response. This paper develops a model of airport pricing that captures a number of these features. The model in particular reflects (1) that airlines typically have market power and are engaged in oligopolistic competition at different sub-markets; (2) that part of external travel delays that aircraft impose are internal to an operator and hence should not be accounted for in congestion tolls; and (3) that different airports in an international network will typically not be regulated by the same authority. We present an analytical treatment for a simple two-node network and some numerical results to illustrate our findings. Some main conclusions are that second-best optimal tolls are typically lower than what would be suggested by congestion costs alone and may even be negative, and that cooperation between regulators need not be stable but that non-cooperation may lead to welfare losses also when compared to a no-tolling situation.