  We consider a class of differential-algebraic equations (DAEs) with index
zero in an infinite dimensional Hilbert space. We define a space of consistent
initial values, which lead to classical continuously differential solutions for
the associated DAE. Moreover, we show that for arbitrary initial values we
obtain mild solutions for the associated problem. We discuss the asymptotic
behaviour of solutions for both problems. In particular, we provide a
characterisation for exponential stability and exponential dichotomies in terms
of the spectrum of the associated operator pencil.
