We discuss Bogomol’nyi equations for general gauge theories (depending on the two Maxwell invariants F^µνF_µν and F˜^µνF_µν) 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.Facultad de Ciencias Exactas