Optimal solution of classes of Mayer problems with feedback linearizable state equations possess unique structures. A number of special numerical algorithms are available to construct their optimal solution. In this paper, we investigate the following question: What classes of optimal control Lagrange problems can be transformed to Mayer problems with feedback linearized state equations?. Using the results of this question, the structure of the optimal solution for a Mayer problem can be extended to the solution of the original Lagrange problem.