  We have calculated self-consistent equilibria of a collisionless relativistic
electron-positron gas in the vicinity of a magnetic $X-$point. For the
considered conditions, pertinent to extra-galactic jets, we find that leptons
are accelerated up to Lorentz factors $\Gamma_0 = \kappa e B_0L {\cal E}^2
/mc^2 \gg 1$, where $B_0$ is the typical magnetic field strength, ${\cal
E}\equiv E_0/B_0$, with $E_0$ the reconnection electric field, $L$ is the
length scale of the magnetic field, and $\kappa \approx 12$. The acceleration
is due to the dominance of the electric field over the magnetic field in a
region around the $X-$point. The distribution function of the accelerated
leptons is found to be approximately $dn/d\gamma \propto \gamma^{-1}$ for
$\gamma \lesssim \Gamma_0$. The apparent distribution function may be steeper
than $\gamma^{-1}$ due to the distribution of $\Gamma_0$ values and/or the
radiative losses. Self-consistent equilibria are found only for plasma inflow
rates to the $X-$point less than a critical value.
