The higher orders instability of a gas cylinder ambient with an incompressible inviscid liquid endowed with surface tension is analyzed. The perturbation equations up to third order are derived and solved. The surface displacements, the velocity potentials and the dispersion relations are derived for each order of axisymmetric perturbation. It is found that, up to third order, a transition from instability to stability states occurs when the perturbed wavelength equals the circumference of the gas cylinder. The stability discussions for the present model have been done and for the nonhollow jet as well. The hollow jet instability is much larger than that of the nonhollow model. It is found that the maximum temporal ampliflcation prevailing in the hollow jet is much higher than that of the full ∞uid jet. These results are consistent with some data of the experimental work of Kendall [9], in the flrst order perturbation.