  We study the initial-boundary value problem for the coupled
Klein-Gordon-Schr\"{o}dinger equations in a domain in $\mathbb R^N$ with $N
\leq 4$. Under natural assumptions on the initial data, we prove the existence
and uniqueness of global solutions in $H^2 \oplus H^2 \oplus H^1$. The method
of the construction of global strong solutions depends on the proof that
solutions of regularized systems by the Yosida approximation form a bounded
sequence in $H^2 \oplus H^2 \oplus H^1$ and a convergent sequence in $H^1
\oplus H^1 \oplus L^2$. The method of proof is independent of the
Brezis-Gallouet technique and a compactness argument.
