  We evaluate the polarization observables I^S and I^C for the reaction gamma p
--> pi^0 eta p, using a chiral unitary framework developed earlier. The I^S and
I^C observables have been recently measured for the first time by the
CBELSA/TAPS collaboration. The theoretical predictions of I^S and I^C, given
for altogether 18 angle dependent functions, are in good agreement with the
measurements. Also, the asymmetry dSigma/dcos(theta) evaluated here agrees with
the data. We show the importance of the Delta(1700)D33 resonance and its S-wave
decay into eta Delta(1232). The result can be considered as a further
confirmation of the dynamical nature of this resonance. At the highest
energies, deviations of the predictions from the data start to become
noticeable, which leaves room for additional processes and resonances such as a
Delta(1940)D33. We also point out how to further improve the calculation.
