  Consider a general nonlinear optimal control problem in finite dimension,
with constant state and/or control delays. By the Pontryagin Maximum Principle,
any optimal trajectory is the projection of a Pontryagin extremal. We establish
that, under appropriate assumptions, Pontryagin extremals depend continuously
on the parameter delays, for adequate topologies. The proof of the continuity
of the trajectory and of the control is quite easy, however, for the adjoint
vector, the proof requires a much finer analysis. The continuity property of
the adjoint with respect to the parameter delay opens a new perspective for the
numerical implementation of indirect methods, such as the shooting method. We
also discuss the sharpness of our assumptions.
