  A gauge theory of second order in the derivatives of the auxiliary field is
constructed following Utiyama's program. A novel field strength $G=\partial
F+fAF$ arises besides the one of the first order treatment, $F=\partial
A-\partial A+fAA$. The associated conserved current is obtained. It has a new
feature: topological terms are determined from local invariance requirements.
Podolsky Generalized Eletrodynamics is derived as a particular case in which
the Lagrangian of the gauge field is $L_{P}\propto G^{2}$. In this application
the photon mass is estimated. The SU(N) infrared regime is analysed by means of
Alekseev-Arbuzov-Baikov's Lagrangian.
