Aircraft Cruise Performance is examined by using energy-state modelling to investigate fuel-range optimal trajectories. Chattering controls are considered appropriate when the hodograph is non-convex. Classical steady-state cruise, simple chattering-cruise and the extended chattering-cruise models are studied as constrained parameter-optimization problems. The term "extended chattering" refers to vehicle system modelling extended to maintain vertical equilibrium only on the average. Numerical solution is obtained using a variable-metric gradient-protection algorithm and computational results are presented for three different aircraft. This study shows that simple chattering cruise for certain specific energies can result in substantial fuel savings over classical steady-state cruise. However extended chattering cruise results in only marginal fuel savings when compared to simple chattering cruise. / Master of Science