We define and then study the structural controllability and observability for a class of complex networks whose dynamics are governed by the nonlinear balance equations. Although related notions of observability for such complex networks have been studied before and in particular, necessary conditions have been reported to select sensor nodes in order to render such a given network observable, there still remain various challenging open problems, especially from the systems and control point of view. The reason is partly that driver and sensor node selection problems for nonlinear complex networks have not been studied systematically, which differs greatly from the relatively comprehensive mathematical development for the linear counterpart. In this paper, based on our refined notions of structural controllability and observability, we construct their necessary conditions for nonlinear complex networks, which are further applied to those networks governed by nonlinear balance equations in order to develop a systematic driver node selection method. Furthermore, we establish a connection between our necessary conditions for structural observability and the conventional sensor node selection method.