  We present complete analytical ${\mathcal O}(\epsilon^2)$ results on the
one-loop amplitudes relevant for the NNLO quark-parton model description of the
hadroproduction of heavy quarks as given by the so-called loop-by-loop
contributions. All results of the perturbative calculation are given in the
dimensional regularization scheme. These one-loop amplitudes can also be used
as input in the determination of the corresponding NNLO cross sections for
heavy flavor photoproduction, and in photon-photon reactions.
