We have succeeded in obtaining exact configurations of irrotational binary systems for compressible ( polytropic ) equations of state .
Our models correspond to binaries of equal mass neutron star systems in the viscosity free limit .
By using the obtained sequences of stationary states , the evolution of binary systems of irrotational neutron stars due to gravitational wave emission has been examined .
For inviscid binary systems the spin angular velocity of each component in a detached phase is smaller than the orbital angular velocity at a contact phase .
Thus the irrotational approximation during evolution of binary neutron stars due to gravitational wave emission can be justified .
Our computational results show that the binary will never reach a dynamically unstable state before a contact phase even for rather stiff polytropes with the index N \ga 0.7 , as the separation of two components decreases due to gravitational wave emission .
This conclusion is quantitatively different from that of Lai , Rasio & Shapiro who employed approximate solutions for polytropic binary systems .