  Differential equations with state-dependent delays define a semiflow of
continuously differentiable solution operators in general only on the
associated {\it solution manifold} in the Banach space
$C^1_n=C^1([-h,0],\mathbb{R}^n)$. For a prototypic example we develop a new
proof that its solution manifold is diffeomorphic to an open subset of the
subspace given by $\phi'(0)=0$, without recourse to a restrictive hypothesis
about the form of delays which is instrumental in earlier work on the nature of
solution manifolds. The new proof uses the framework of algebraic-delay
systems.
