The paper studies inference in nonlinear models where identification loss presents in multiple parts of the parameter space. For uniform inference, we develop a local limit theory that models mixed identification strength. Building on this non-standard asymptotic approximation, we suggest robust tests and confidence intervals in the presence of non-identified and weakly identified nuisance parameters. In particular, this covers applications where some nuisance parameters are non-identified under the null (Davies (1977, 1987)) and some nuisance parameters are subject to a full range of identification strength. The asymptotic results involve both inconsistent estimators that depend on a localization parameter and consistent estimators with different rates of convergence. A sequential argument is used to peel the criterion function based on identification strength of the parameters. The robust test is uniformly valid and non-conservative.