  Frequency-modulation (FM) spectroscopy has been extended to the
vacuum-ultraviolet (VUV) range of the electromagnetic spectrum. Coherent VUV
laser radiation is produced by resonance-enhanced sum-frequency mixing
($\nu_{\mathrm{VUV}}=2\nu_{\mathrm{UV}}+\nu_2$) in Kr and Xe using two
near-Fourier-transform-limited laser pulses of frequencies $\nu_{\mathrm{UV}}$
and $\nu_2$. Sidebands generated in the output of the second laser ($\nu_2$)
using an electro-optical modulator operating at the frequency
$\nu_{\mathrm{mod}}$ are directly transfered to the VUV and used to record FM
spectra. Demodulation is demonstrated both at $\nu_{\mathrm{mod}}$ and
$2\nu_{\mathrm{mod}}$. The main advantages of the method are that its
sensitivity is not reduced by pulse-to-pulse fluctuations of the VUV laser
intensity, compared to VUV absorption spectroscopy is its background-free
nature, the fact that its implementation using table-top laser equipment is
straightforward and that it can be used to record VUV absorption spectra of
cold samples in skimmed supersonic beams simultaneously with
laser-induced-fluorescence and photoionization spectra. To illustrate these
advantages we present VUV FM spectra of Ar, Kr, and N$_2$ in selected regions
between 105000cm$^{-1}$ and 122000cm$^{-1}$.
