High-order well-balanced WENO schemes have already been developed for hyperbolic conservation laws (see for example [4] ), where the effects of convective fluxes and source terms cancel each other for still water and for moving shallow water(see for example. [5]). Different strategies have been discussed in the literature to extend high-order WENO finite-difference methods to hyperbolic systems with source terms and/or non-conservative products. In [2], a strategy based on the so-called Local Flux approach was introduced. In this framework, source terms and non- conservative products are represented as the derivative of a generalized flux function that, unlike the Global Flux approach [1], is defined locally based on the choice of a family of paths. Two different techniques were proposed in that work to achieve the well-balanced property. First, the technique de- veloped in [3], based on the computation of local equilibria, was extended. Second, a method relying on an appropriate choice of the family of paths was introduced. This strategy allows non-conservative products to be written as the derivative of a generalized flux function that is defined locally on the basis of the selected family of paths. WENO reconstructions are then applied to this generalized flux. The goal of this work is to further investigate this approach, which in principle allows the design of well- balanced methods without the additional computational cost associated with computing local equilibria. The approach is tested to different hyperbolic systems like the Burger’s equations, the nonlinear shallow water equations and the two layer shallow water equations.