  We show that for a system $$ x'(t)=g(x(t-d_1(Lx_t)),\dots,x(t-d_k(Lx_t))) $$
of $n$ differential equations with $k$ discrete state-dependent delays the
solution manifold, on which solution operators are differentiable, is nearly as
simple as a graph over a closed subspace in $C^1([-r,0],\mathbb{R}^n)$. The map
$L$ is continuous and linear from $C([-r,0],\mathbb{R}^n)$ onto a
finite-dimensional vectorspace, and $g$ as well as the delay functions
$d_{\kappa}$ are assumed to be continuously differentiable.
