The problem of assigning gates to aircraft that are due to arrive at an airport is one that involves a dynamic task environment. Airport gates can only be assigned if they are currently available, but deciding which gate to assign to which flight also involves satisfying multiple additional constraints. Once a solution has been found, new incoming flights will have approached the airspace of the airport in question, and these will require arrival gates to be assigned to them, so the entire process must be repeated. These observations have led us to propose a coevolutionary model for automating the airport gate scheduling problem. We represent the genotypes of two species. One species corresponds to the current problem to be addressed (a list of departing and arriving flights at a given time-step) and the other species corresponds to the solutions being proposed for that problem (a list of possible gate assignments for the arriving flights). An evolutionary algorithm which operates on a population of solution genotypes is used to solve each instance of the airport gate scheduling problem. A coevolutionary algorithm in which the two species influence each other, which incorporates the previously-mentioned evolutionary algorithm once at each time-step, models the fact that multiple instances of the problem occur over time as an airport operates.