  Studied here is the generalized Benjamin-Ono--Zakharov-Kuznetsov equation
$u_t+u^pu_x+\alpha\mathscr{H}u_{xx}+\varepsilon u_{xyy}=0, \quad
(x,y)\in\rr^2\!,\;\;t\in \rr^+\!$ in two space dimensions. Here, $\mathscr{H}$
is the Hilbert transform and subscripts denote partial differentiation. We
classify when equation (1) possesses solitary-wave solutions in terms of the
signs of the constants $\alpha$ and $\varepsilon$ appearing in the dispersive
terms and the strength of the nonlinearity. Regularity and decay properties of
these solitary wave are determined and their stability is studied.
