  We introduce discontinuous solutions to nonlinear impulsive control systems
with state time delays in the dynamics and derive necessary optimality
conditions in the form of a Maximum Principle for associated optimal control
problems. In the case without delays, if the measure control is scalar valued,
the corresponding discontinuous state trajectory, understood as a limit of
classical state trajectories for absolutely continuous controls approximating
the measure, is unique. For vector valued measure controls however, the
limiting trajectory is not unique and a full description of the control must
include additional `attached' controls affecting instantaneous state evolution
at a discontinuity. For impulsive control systems with time delays we reveal a
new phenomenon, namely that the limiting state trajectory resulting from
different approximations of a given measure control needs not to be unique,
even in the scalar case. Correspondingly, our framework allows for additional
attached controls, even though the measure control is scalar valued.
