  We calculate the dynamical structure factors of the magnetization-plateau
state in the $S=1/2$ bond-alternating spin chain with a next-nearest-neighbor
interaction. The results show characteristic behaviors depending on the
next-nearest-neighbor interaction $\alpha$ and the bond-alternation $\delta$.
We discuss the lower excited states in comparison with the exact excitation
spectrums of an effective Hamiltonian. From the finite size effects,
characteristics of the lowest excited states are investigated. The
dispersionless mode of the lowest excitation appears in adequate sets of
$\alpha$ and $\delta$, indicating that the lowest excitation is localized
spatially and forms an isolated mode below the excitation continuum. We further
calculate the static structure factors. The largest intensity is located at
$q=\pi$ for small $\delta$ in fixed $\alpha$. With increasing $\delta$, the
wavenumber of the largest intensity shifts towards $q=\pi/2$, taking the
incommensurate value.
