  In this paper we investigate a parametric resonance phenomenon of a
Kaluza-Klein mode in a $D$-dimensional generalized Kaluza-Klein theory. As the
origin of the parametric resonance we consider a small oscillation of a scale
of the compactification around a today's value of it. To make our arguments
definite and for simplicity we consider two classes of models of the
compactification: those by $S_{d}$ ($d=D-4$) and those by $S_{d_{1}}\times
S_{d_{2}}$ ($d_1\ge d_2$, $d_{1}+d_{2}=D-4$). For these models we show that
parametric resonance can occur for the Kaluza-Klein mode. After that, we give
formulas of a creation rate and a number of created quanta of the Kaluza-Klein
mode due to the parametric resonance, taking into account the first and the
second resonance band. By using the formulas we calculate those quantities for
each model of the compactification. Finally we give conditions for the
parametric resonance to be efficient and discuss cosmological implications.
