  The method of asymptotic normalization coefficients is a standard approach
for studies of two-body non-resonant radiative capture processes in nuclear
astrophysics. This method suggests a fully analytical description of the
radiative capture cross section in the low-energy region of the astrophysical
interest. We demonstrate how this method can be generalized to the case of
three-body $2p$ radiative captures. It was found that an essential feature of
this process is the highly correlated nature of the capture. This reflects the
complexity of three-body Coulomb continuum problem. Radiative capture
$^{15}$O+$p$+$p \rightarrow ^{\,17}$Ne+$\gamma$ is considered as an
illustration.
