This paper discusses the optimal solution of Mayer's problem for globally f
eedback linearizable systems subject to general nonlinear path and actuator
constraints. This class of problems includes the minimum time problem, imp
ortant for engineering applications. Globally feedback linearizable nonline
ar systems are diffeomorphic to linear systems that consist of blocks of in
tegrators. Using this alternate form, it is proved that the optimal solutio
n always lies on a constrain arc. As a results of this optimal structure of
the solution, efficient numerical procedures can be developed. For a singl
e input system, this result allows to characterize and build the optimal so
lution. The associated multi-point boundary value problem is then solved us
ing direct solution techniques.