  A free differential algebra is generalization of a Lie algebra in which the
mathematical structure is extended by including of new Maurer-Cartan equations
for higher-degree differential forms. In this article, we propose a
generalization of the Chern-Weil theorem for free differential algebras
containing only one $p$-form extension. This is achieved through a
generalization of the covariant derivative, leading to an extension of the
standard formula for Chern-Simons and transgression forms. We also study the
possible existence of anomalies originated on this kind of structure. Some
properties and particular cases are analyzed.
