  In this paper we study the initial-value problem associated with the
Benjamin-Ono-Zakharov-Kuznetsov equation. Such equation appears as a
two-dimensional generalization of the Benjamin-Ono equation when transverse
effects are included via weak dispersion of Zakharov-Kuznetsov type. We prove
that the initial-value problem is locally well-posed in the usual
$L^2(\R^2)$-based Sobolev spaces $H^{s}(\R^2)$, $s>11/8$, and in some weighted
Sobolev spaces. To obtain our results, most of the arguments are accomplished
taking into account the ones for the Benjamin-Ono equation.
