Aircraft conflict detection and resolution is crucial in Air Traffic Management to guarantee air traffic safety. When aircraft sharing the same airspace are too close to each other according to their predicted trajectories, separation maneuvers have to be performed to avoid risks of collision. We propose new mixed-integer Nonlinear optimization models combining turn-changes and velocity-changes separation maneuvers. These separation maneuvers are performed by each aircraft at instant times which are decision variables of the problem, and each aircraft is allowed to perform only one type of maneuver. The pros and cons of the models are discussed.