The instability of the von Ka´rma´n vortex streets and the existence of a global Lyapunov function at the special aspect ratioh/l=(1/&pgr;)sinh−1(1), are some of the difficulties with the well‐known von Ka´rma´n model. By consistently applying the principle of genericity, its shown that a new family of near‐equilibrium periodic solutions of the von Ka´rma´n model for aspect ratios near 0.281... supplies numerous theoretical candidates for observed vortex trails. This set of solutions implies that there is no global Lyapunov functions whenh/l≠(1/&pgr;)sinh−1(1) which in turn leads to a rich variety of near‐equilibrium solutions for the model.