Collision avoidance for multiple aircraft can be stated as a problem ofmaintaining safe distance between aircraft in conflict. Optimal collision avoidanceproblem seeks to minimize the given cost function while simultaneously satisfyingconstraints. The cost function could be a function of time or control input. This paperaddresses the trajectory time-optimization problem for collision avoidance ofunmanned aerial vehicles(UAVs). The problem is difficult to handle in general due tothe two-point boundary value problem subject to dynamic environments. Somesimplifying aleorithms are used for potential applications in on-line operation.Although under possibility of more complicated problems, a dynamic problem istransformed into a static one by prediction of the conflict time and some appropriateassumptions.