Abstract: Here some ideas about reduction for principal bundles are

presented. It is known that Classical Field theories of first order can

be formulated as Lagrangian submanifolds of premultisymplectic manifolds

through a particular Tulczyjew's Triple. In the case, the Classical Field

theories is a G-principal bundle a new triple and new Lagrangian

submanifolds related with the previous ones are obtained to formulated

the Euler-Poincare and the Hamilton-Poincare equations when the

Lagrangian and the Hamiltonian density are G-invariant.