  Deeply-virtual Compton scattering gives access to the generalized parton
distributions that encode the information on the transverse position of quarks
and gluons in the proton in dependence in their longitudinal momentum. In
anticipation of the high-precision experimental data in a broad kinematic range
from the Electron-Ion Collider, we have calculated the two-loop,
next-to-next-to-leading (NNLO) DVCS coefficient functions associated with the
dominant Compton form factors $\mathcal H$ and $\mathcal E$ at large energies.
The NNLO correction to the imaginary part of $\mathcal H$ appears to be rather
large, up to factor two at the input scale $Q^2=4$ GeV$^2$ for simple GPD
models, due to a cancellation between quark and gluon contributions.
