Abstract: Under the assumption of slender body,starting from Oswatitschs non-viscous transonic axisymmetric irrotational basic equation,the motion equation of physical plane is transferred to hodograph equation in simpler form by new variables.Then,the latter is integrated by the conditions in the vicinity of the sonic line and the analytic solution can be acquired. And then,a characteristic equation in the vicinity of the sonic line is derived by Courant’s theo- ry,which is an analytic expression. It indicates that there are two families of characteristics and they are all curves of 2/ 3 power.

Key words: axisymmetric flow, transonic flow, characteristic equations