  We construct the Bardeen anomaly and its related Wess-Zumino term in the
supersymmetric standard model. In particular we show that it can be written in
terms of a composite linear superfield related to supersymmetrized Chern-Simons
forms, in very much the same way as the Green-Schwarz term in four-dimensional
string theory. Some physical applications, such as the contribution to the g-2
of gauginos when a heavy top is integrated out, are briefly discussed.
