  The increasing accuracy of current and planned experiments to measure the
anomalous magnetic moment of the muon requires more precision and reliability
of its theoretical calculation. For this purpose, we calculate the differential
cross section for the process of annihilation of an electron-positron pair into
two photons, one of which is virtual, accompanied by the emission of soft
photons, taking into account radiative corrections of the order $\alpha^2$. The
results obtained can be used to improve the accuracy of calculating the
contribution of the hadron vacuum polarization to the muon anomalous moment. It
is shown that all logarithmically amplified two-loop corrections can be easily
found using modern theorems of soft and collinear factorizations and available
one-loop results.
