  We study the analyticity of bounded solutions of systems of analytic
state-dependent delay differential equations. We obtain the analyticity of
solutions by transforming the system of state-dependent delay equations into an
abstract ordinary differential equation in a subspace of the sequence space
$l^{\infty}(\mathbb{R}^{N+1})$ and prove the existence of complex extension of
the bounded solutions. An example is given to illustrate the general results.
