  We introduce a notion of bounded variation solution for a new class of
nonlinear control systems with ordinary and impulsive controls, in which the
drift function depends not only on the state, but also on its past history,
through a finite number of time delays. After proving the well posedness of
such solutions and the continuity of the corresponding input output map with
respect to suitable topologies, we establish necessary optimality conditions
for an associated optimal control problem. The approach, which involves
approximating the problem by a non impulsive optimal control problem with time
delays and using Ekeland principle combined with a recent, nonsmooth version of
the Maximum Principle for conventional delayed systems, allows us to deal with
mild regularity assumptions and a general endpoint constraint.
