  We investigate the generation of gravitational waves in the hybrid
quintessential inflationary model. The full gravitational-wave energy spectrum
is calculated using the method of continuous Bogoliubov coefficients. The
post-inflationary kination period, characteristic of quintessential
inflationary models, leaves a clear signature on the spectrum, namely, a peak
at high frequencies. The maximum of the peak is firmly located at the MHz-GHz
region of the spectrum and corresponds to $\Omega_{GW} \simeq 10^{-12}$. This
peak is substantially smaller than the one appearing in the gravitational-wave
energy spectrum of the original quintessential inflationary model, therefore
avoiding any conflict with the nucleosynthesis constraint on
$\Omega_\Omega_{GW}$.
