  In this work we evaluate the physical acceptability of relativistic
anisotropic spheres modeled by two polytropic equations of state -- with the
same newtonian limit -- commonly used to describe compact objects in General
Relativity. We integrate numerically the corresponding Lane-Emden equation in
order to get density, mass and pressure profiles. An ansatz is used for the
anisotropic pressure allowing us to have material configurations slightly
deviated from isotropic condition. Numerical models are classified in a
parameter space according to the number of physical acceptability conditions
that they fulfil. We found that the polytropes considering total energy density
are more stable than the second type of polytropic EoS.
