Abstract: In this paper we have established a superspace U for supergauge actions, constructed a confermal supergroup SU (2, 2|N) and a conformal extended SU (2, 2|N) supergravity theory. Using the Lagrangian Higgs evolution mechanism under the supergroup SU(2, 2|N)⊗SU(N) actions on the superspace U, we have advanced a SU(2, 2|N)⊗ SU<N'> superunified theory of a superunited system, discussed the Lagrangian evolution of the superunified theory, and given the fiber bundle geometry of all above mechanisms.