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The Conflict Detection and Resolution Problem for Air Traffic Flow Management consists of deciding the best strategy for airborne aircraft so that there is guarantee that no conflict takes place, i.e., all aircraft maintain the minimum safety distance at every time instant. Two integer linear optimization models for conflict avoidance between any number of aircraft in the airspace are proposed, the first being a pure 0-1 linear which avoids conflicts by means of altitude changes, and the second a mixed 0-1 linear whose strategy is based on altitude and speed changes. Several objective functions are established. Due to the small elapsed time that is required for solving both problems, the approach can be used in real time by using state-of-the-art mixed integer linear optimization software.