  We introduce and discuss Fr\'echet differentiability for maps between
Fr\'echet spaces. For delay differential equations $x'(t)=f(x_t)$ we construct
a continuous semiflow of continuously differentiable solution operators
$x_0\mapsto x_t$, $t\ge0$, on submanifolds of the Fr\'echet space
$C^1((-\infty,0],\mathbb{R}^n)$, and establish local invariant manifolds at
stationary points by means of transversality and embedding properties. The
results apply to examples with unbounded but locally bounded delay.
