We study the evolution of the families of double- and triple-periodic orbits in a dynamical system that has closed zero velocity curves for arbitrarily large energies. We find three interesting features: (i) the characteristic \(x=x(h)\) of the family of double periodic orbits divides the (x,h)-plane into two unconnected parts; (ii) there is a sequence of sixteen closed characteristics, bifurcating from another one, each of them inside the previous one; (iii) inside the innermost characteristic of that sequence there is a sequence of eight pairs of close characteristics which are not connected with any of the previous characteristics.