  We study integro-differential inclusions in Hilbert spaces with
operator-valued kernels and give sufficient conditions for the well-posedness.
We show that several types of integro-differential equations and inclusions are
covered by the class of evolutionary inclusions and we therefore give criteria
for the well-posedness within this framework. As an example we apply our
results to the equations of visco-elasticity and to a class of nonlinear
integro-differential inclusions describing Phase Transition phenomena in
materials with memory.
