  We present a general analysis of gauge invariant, exact and metric
independent forms which can be constructed using higher rank field-strength
tensors. The integrals of these forms over the corresponding space-time
coordinates provides new topological Lagrangians. With these Lagrangians one
can define gauge field theories which generalize the Chern-Simons quantum field
theory. We also present explicit expressions for the potential gauge anomalies
associated with the tensor gauge fields and classify all possible anomalies
that can appear in lower dimensions. Of special interest are those which can be
constructed in four, six, eight and ten dimensions.
