  Axions are the natural consequence of the introduction of the Peccei-Quinn
symmetry to solve the strong CP problem. All the efforts to detect such elusive
particles have failed up to now. Nevertheless, it has been recently shown that
the luminosity function of white dwarfs is best fitted if axions with a mass of
a few meV are included in the evolutionary calculations. Our aim is to show
that variable white dwarfs can provide additional and independent evidence
about the existence of axions. The evolution of a white dwarf is a slow cooling
process that translates into a secular increase of the pulsation periods of
some variable white dwarfs, the so-called DAV and DBV types. Since axions can
freely escape from such stars, their existence would increase the cooling rate
and, consequently, the rate of change of the periods as compared with the
standard ones. The present values of the rate of change of the pulsation period
of G117-B15A are compatible with the existence of axions with the masses
suggested by the luminosity function of white dwarfs, in contrast with previous
estimations. Furthermore, it is shown that if such axions indeed exist, the
drift of the periods of pulsation of DBV stars would be noticeably perturbed.
