The main result of this paper is an approximation theorem of Mergelyan type for solutions of the generalized Vekua equation \(Lu = Au + B \overline{u}\) where L belongs to a class of degenerate elliptic planar vector fields and \(A,B \in L^{p}\) . Throughout the paper these solutions are called generalized analytic functions and we also prove an Arakelian type theorem for them. As an application, we study the behavior of radial limits of generalized analytic functions on the disk and solve a Riemann-Hilbert type problem for the equation \(Lu = Au + B \overline{u} + f\) on the upper half-plane.
