We study equilibrium sequences of close binary systems composed of identical polytropic stars in Newtonian gravity .
The solving method is a multi-domain spectral method which we have recently developed .
An improvement is introduced here for accurate computations of binary systems with stiff equation of state ( \gamma > 2 ) .
The computations are performed for both cases of synchronized and irrotational binary systems with adiabatic indices \gamma = 3 ,~ { } 2.5 ,~ { } 2.25 ,~ { } 2 and 1.8 .
It is found that the turning points of total energy along a constant-mass sequence appear only for \gamma \geq 1.8 for synchronized binary systems and \gamma \geq 2.3 for irrotational ones .
In the synchronized case , the equilibrium sequences terminate by the contact between the two stars .
On the other hand , for irrotational binaries , it is found that the sequences terminate at a mass shedding limit which corresponds to a detached configuration .