Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In this paper we study the initial-value problem associated with the Benjamin-Ono-Zakharov-Kuznetsov equation. We prove that the IVP for such equation is locally well-posed in the usual Sobolev spaces H-s (R-2), s > 2, and in the anisotropic spaces H-s1,H-s2 (R-2), s(2) > 2, s(1) >= s(2). We also study the persistence properties of the solution and local well-posedness in the weighted Sobolev class Z(s,r) = H-s (R-2) boolean AND L-2 ((1 + x(2) + y(2))(tau) dx dy), where s > 2, r >= 0, and s >= 2r. Unique continuation properties of the solution are also established. These continuation principles show that our persistence properties are sharp. (C) 2014 Elsevier Inc. All rights reserved.4172660693UFG - Campus Jatai, BrazilConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)CNPq [301535/2010-8]FAPESP [2013/08050-7]