  We discuss Bogomol'nyi equations for general gauge theories (depending on the
two Maxwell invariants $F^{\mu \nu} F_{\mu \nu}$ and $\tilde F^{\mu \nu} F_{\mu
\nu}$) coupled to Higgs scalars. By analysing their supersymmetric extension,
we explicitly show why the resulting BPS structure is insensitive to the
particular form of the gauge Lagrangian: Maxwell, Born-Infeld or more
complicated non-polynomial Lagrangians all satisfy the same Bogomol'nyi
equations and bounds which are dictated by the underlying supersymmetry
algebra.
