  Differential equations with state-dependent delays define a semiflow of
continuously differentiable solution operators in general only on an associated
submanifold of the Banach space $C^1([-h,0],\mathbb{R}^n)$. We extend a recent
result on simplicity of these {\it solution manifolds} to systems where the
delay is given by the state only implicitly in an extra equation. Such
algebraic-delay systems arise from various applications.
  Key words: Delay differential equation, implicit state-dependent delay,
solution manifold
