  We study abstract linear and nonlinear evolutionary systems with single or
multiple delay feedbacks, illustrated by several concrete examples. In
particular, we assume that the operator associated with the undelayed part of
the system generates an exponentially stable semigroup and that the delay
damping coefficients are locally integrable in time. A step by step procedure
combined with Gronwall's inequality allows us to prove the existence and
uniqueness of solutions. Furthermore, under appropriate conditions we obtain
exponential decay estimates.
