  The form of higher-spin current interactions in the sector of one-forms is
derived from the nonlinear higher-spin equations in $AdS_4$. Quadratic
corrections to higher-spin equations are shown to be independent of the phase
of the parameter $\eta =\exp i\varphi$ in the full nonlinear higher-spin
equations. The current deformation resulting from the nonlinear higher-spin
equations is represented in the canonical form with the minimal number of
space-time derivatives. The non-zero spin-dependent coupling constants of the
resulting currents are determined in terms of the higher-spin coupling constant
$\eta\bar\eta$. Our results confirm the conjecture that (anti-)self-dual
nonlinear higher-spin equations result from the full system at ($\eta=0$) $\bar
\eta=0$.
