  We investigate the QED Compton process (QEDCS) in $e p \to e \gamma p$ and $e
p \to e \gamma X$, together with the major background coming from the virtual
Compton scattering (VCS), where the photon is emitted from the hadronic vertex.
We suggest new kinematical constraints which suppress the VCS background and
are furthermore suitable for the extraction of the equivalent photon content of
the proton at the HERA collider. We show that the cross section, commonly
expressed in terms of the proton structure functions, is reasonably well
described by the equivalent photon approximation of the proton, also in the
inelastic channel in the proposed kinematical region.
