AbstractThe structure of singularities of the Veneziano amplitude in the complex angular momentum plane is studied. The introduction of a nonlinear term in the trajectory essentially changes the properties of the partial amplitude as compared to the case of linear trajectories. In theJ‐plane, besides simple poles lying on the leading and on the conventional daughter trajectories, additional poles lying on mirage trajectories (situated below the leading trajectory) emerge. In the partial amplitude also non‐reggeised poles in thes‐plane emerge whose position is independent of the angular momentum. Such are, for example, the ance