  The problem of computing systematically the gauge invariant extension of WZW
term through equivariant cohomology is addressed. The analysis done by Witten
in the two-dimensional case is extended to the four-dimensional ones. While
Cartan's model is used to find the anomaly cancelation condition. It is shown
that the Weil model is more appropriated to find the gauge invariant extension
of the WZW term. In the process we point out that Weil's and Cartan's models
are also useful to stress some connections with the abelian anomaly.
