Congestion games–in which players strategically choose from a set of ?resources? and derive utilities that depend on the congestion on each resource– are important in a wide range of applications. However, to date, such games have been constrained to use utility functions that are linear sums with respect to resources. To remove this restriction, this paper provides a significant generalisation to the case where a player?s payoff can be given by any real-valued function over the set of possible congestion vectors. Under reasonable assumptions on the structure of player strategy spaces, we constructively prove the existence of a pure strategy equilibrium for the very wide class of these generalised games in which player utility functions are congestion-averse–i.e., monotonic, submodular and independent of irrelevant alternatives. Although, as we show, these games do not admit a generalised ordinal potential function (and hence–the finite improvement property), any such game does possess a Nash equilibrium in pure strategies. A polynomial time algorithm for computing such an equilibrium is presented.