Some properties of the Regge trajectories are investigated on the basis of the principle of maximum analyticity. It has been shown that the Regge trajectories corresponding to the different particles are monotonic increasing functions of energy below the threshold and the asymptotic limits of every trajectory are the same for t→±∞. In particular, the vacuum Regge trajectory has nonlinear feature when -t0p(0) must satisfy the inequatily 1/t0p(0)0 is thevalue of t when αp(t=-t0)=0.