Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Studied here is the generalized Benjamin-Ono-Zalcharov-Kuznetsov equation u(t) + u(p)u(x) + alpha Hu(xx) + epsilon u(xyy) = 0, (x, y) is an element of R-2, t is an element of R+, in two space dimensions. Here, A is the Hilbert transform and subscripts denote partial differentiation. We classify when this equation possesses solitary-wave solutions in terms of the signs of the constants alpha and epsilon appearing in the dispersive terms and the strength of the non-linearity. Regularity and decay properties of these solitary wave are determined and their stability is studied.209/Out 801834research council of Damghan [93/MATH/125/227]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)University of Illinois at ChicagoConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)