  We develop techniques to classify D- and F-flat directions for N=1
supersymmetric string vacua of the perturbative heterotic string theory, which
possess an anomalous U(1) gauge group at the tree level. Genus-one corrections
generate a Fayet-Iliopoulos term for the D-term of U(1)_A, which is canceled by
non-zero vacuum expectation values (VEVs) of certain massless multiplets in
such a way that the anomalous U(1) is broken, while maintaining the D- and
F-flatness of the effective field theory. A systematic analysis of flat
directions is given for non-zero VEVs of non-Abelian singlets, and the
techniques are illustrated for a specific model. The approach sets the stage to
classify the D- and F-flat directions for a large class of perturbative string
vacua. This classification is a prerequisite to address systematically the
phenomenological consequences of these models.
