A nonlinear perturbation method is developed to solve the problem of correlating a finite element model (FEM) to a structure for which an incomplete set of natural frequencies and mode shapes and/or some static deflections have been measured. The solution algorithm can handle differences between FEM and structure, in design variables and response, as large as 100-300%, depending on the scale of the structure and correlation measures. This is achieved incrementally by making inadmissible predictions, identifying the modal cognate space relevant to the correlation measures, and making admissible corrections in the cognate space. The developed computer code postprocesses results of the FEM modal and/or static analyses of the initial model only. No additional finite element analysis is required. Lagrange multipliers reveal the dominant correlation requirements and the active admissible cognate subspace. Depending on the number of correlation variables and measures, an optimal, a unique, or an inadmissible minimal error solution may be produced. Beam and offshore tower examples are used to test the algorithm and investigate conflicting requirements, definition of admissible cognate space, limits of allowable differences between FEM and structure, accuracy, and cost of the nonlinear perturbation method.