The uniqueness of the solution of the differential equations derived from Pontryagin's Maximum Principle is considered for a general control problem with a freo right end of the trajectory and fixed terminal time. Under several restrictive conditions on the controlled system and performance criterion, it is proved that those equations have a unique solution. This is done by embedding the problem into a class of similar problems by means of the introduction of a positive parameter • multiplying the performance criterion, and then making use of the uniqueness properties of an associated autonomous system together with the continuity of the solutions of the differential equations with respect to the parameter ∈