This paper presents the parallelisation of a Sequential Monte Carlo algorithm, and the associated changes required when applied to the problem of conflict resolution and aircraft trajectory control in air traffic management. The target problem is non-linear, constrained, non-convex and multi-agent. The new method is shown to have a 98.5% computational time saving over that of a previous sequential implementation, with no degradation in path quality. The computation saving is enough to allow real-time implementation.