We introduce methods which seem to be a new and promising tool in hierarchical fixed-point problems. The goal of this note is to analyze the convergence properties of these new types of approximating methods for fixed-point problems. The limit attained by these curves is the solution of the general variational inequality,, where denotes the normal cone to the set of fixed point of the original nonexpansive mapping and a suitable nonexpansive mapping criterion. The link with other approximation schemes in this field is also made.