  We make a theoretical study of the charge and forward-backward pion
asymmetries in the e+e- --> pi+ pi- gamma process on and off the phi resonance
energy. These observables are rather sensitive to the inner details of the
theoretical models to describe the reaction. In addition to the standard
implementation of the initial state radiation (ISR) and the Bremsstrahlung
contribution to the final state radiation (FSR), we use the techniques of the
chiral unitary approach to evaluate the contribution from the mechanisms of phi
decay into pi+pi-gamma. This contribution involves the implementation of final
state interaction from direct chiral loops, the exchange of vector and
axial-vector resonances and the final state interaction through the
consideration of the meson-meson unitarized amplitudes, which where found
important in a previous work describing the phi --> pi pi gamma. We find a good
reproduction of the experimental data from KLOE for the forward-backward
asymmetry, both at the phi peak and away from it. We also make predictions for
the angular distributions of the charge asymmetry and show that this observable
is very sensitive to the chiral loops involved in phi radiative decay.
