Perfect bifurcational dissipative systems with trivial fundamental paths under follower loads in regions of divergence instability, are considered. Such autonomous non potential systems under certain conditions may exhibit limit cycles in critical states of divergence. This is due to the coupling of divergence and flutter instability occurring at a double zero eigenvalue. The conditions for a double zero eigenvalue in critical states of divergence arc properly established. A 2-DOF and 3-DOF systems are used as models to illustrate the new findings.