  We construct stationary axisymmetric solutions of the Euler-Poisson
equations, which govern the internal structure of polytropic gaseous stars,
with small constant angular velocity when the adiabatic exponent $\gamma$
belongs to $(\frac65,\frac32]$. The problem is formulated as a nonlinear
integral equation, and is solved by iteration technique. By this method, not
only we get the existence, but also we clarify properties of the solutions such
as the physical vacuum condition and oblateness of the star surface.
