  We study parametric amplification of Kaluza-Klein (KK) modes in a higher
$D$-dimensional generalized Kaluza-Klein theory, which was originally
considered by Mukohyama in the narrow resonance case. It was suggested that KK
modes can be enhanced by an oscillation of a scale of compactification by the
$d$-dimensional sphere $S^d~(d=D-4)$ and by the direct product $S^{d_1}\times
S^{d_2}~(d_1+d_2=D-4)$. We extend this past work to the more general case where
initial values of the scale of compactification and the quantum number of the
angular momentum $l$ of KK modes are not small. We perform analytic approaches
based on the Mathieu equation as well as numerical calculations, and find that
the expansion of the universe rapidly makes the KK field deviate from
instability bands. As a result, KK modes are not enhanced sufficiently in an
expanding universe in these two classes of models.
