  In this paper, high order well-balanced finite difference weighted
essentially non-oscillatory methods to solve general systems of balance laws
are presented. Two different families are introduced: while the methods in the
first one preserve every stationary solution, those in the second family only
preserve a given set of stationary solutions that depend on some parameters.
The accuracy, well-balancedness, and conservation properties of the methods are
discussed, as well as their application to systems with singular source terms.
The strategy is applied to derive third and fifth order well-balanced methods
for a linear scalar balance law, Burgers' equation with a nonlinear source
term, and for the shallow water model. In particular, numerical methods that
preserve every stationary solution or only water at rest equilibria are derived
for the latter.
