In the usual formulation of nonlinear models (such as chiral models), there is invariance under a nonlinear realization of a group GF which becomes linear when restricted to a subgroup HF. We formulate them so that they become gauge theories for a local group HC. It is the local version of a global group HC. When the gauge transformations are unrestricted at spatial infinity, only HC singlets are observable, and the usual formulation is recovered. When the gauge transformations are required to reduce to identity at spatial infinity, the usual formulation is no longer recovered. In particular, (1) nonsinglets under HC become observable, (2) the classical vacuum becomes degenerate under suitable conditions as in Yang-Mills theories, (3) the spontaneous symmetry breakdown of GF seems complete. (In the usual formulations, GF is broken down only to HF.) It is shown that the instanton and meron solutions of Yang-Mills theories are also solutions of certain nonlinear models. It is also shown that in a certain class of nonlinear models in (Euclidean) (3 + 1)-dimensional space-time, there are no instanton solutions for any choice of the groups. © 1979 The American Physical Society.