This work concerns existence, uniqueness and regularity for the differential-functional equation: \[ y'(t)=A(t)y(t)+B(t)y(t- h)+\int^{0}_{-h}a(\theta)C(t)y(t+\theta)d\theta +f(t) \] in [s,T], \(y(s+\theta)=\phi (\theta)\) for \(\theta\in [-r,0]\) in a Hilbert space H. Here the operator A(t) generates an analytic semigroup for each t and B(.), C(.) are measurable and bounded from [0,T] into the space of Lipschitz continuous operators from a Banach space \(D\hookrightarrow H\) into H. As an example the author studies a class of nonautonomous parabolic equations with delays in derivatives up to the highest order.