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For autonomous delay differential equations $x'(t)=f(x_t)$ we construct acontinuous semiflow of continuously differentiable solution operators$x_0\mapsto x_t$, $t\ge0$, on open subsets of the Fr\'echet space$C((-\infty,0],\mathbb{R}^n)$. For nonautonomous equations this yields acontinuous process of differentiable solution operators. As an application weobtain processes which incorporate all solutions of Volterraintegro-differential equations $x'(t)=\int_0^tk(t,s)h(x(s))ds$

Delay differential equations with differentiable solution operators on  open domains in $C((-\infty,0],\mathbb{R}^n)$, and processes for Volterra  integro-differential equations