  The emission of the hard photon by the initial state is considered. The
nucleon polarization and the differential cross sections for some experimental
conditions have been calculated. The case of the emission of the collinear
(with respect to the direction of the electron beam momentum) photon is
considered separately. The differential cross section, the nucleon
polarization, the correlation coefficients for both polarized nucleons
(provided the electron beam is unpolarized or longitudinally polarized), the
transfer polarization from the longitudinally polarized electron beam to the
nucleon have been calculated. The photon energy distribution for the reaction
$e^+e^-\to h_1h_2\gamma $, where $h_1 $ and $h_2$ are some hadrons for the case
of the collinear photon, emitted in the initial state, has been calculated. As
$h_1h_2$ final state we considered some channels, namely: two spinless mesons
(for example, $\pi^+\pi^-, K^+K^-$), two spin--one particles (for example,
$\rho^+\rho^-, d\bar d$), the $\pi a_1(1260)$ and $\Delta(1232)\bar N$
channels. The photon energy distributions are calculated in terms of the form
factors of the $\gamma^*\to h_1h_2$ transition ($\gamma^*$ is the virtual
photon).
