  We analyze the conditions under which some supersymmetric generalizations of
a class of models descending from string theory allow an axion in the physical
spectrum, due to the presence of anomalous abelian gauge interactions. The
gauge structure of these constructions involve the Stueckelberg supermultiplet
and a supersymmetric version of the Wess-Zumino term for anomaly cancellation.
While these conditions are not satisfied by the MSSM superpotential, we show
that an axion-like particle appears in the spectrum if extra Standard Model
singlets are present. We show that the minimal requirements are met by simple
superpotentials in which the singlet superfield is charged under the anomalous
U(1). The dark matter sector of these models include an axion and several
neutralinos with an axino component.
