  Star-forming galaxies at high redshifts are the ideal targets to probe the
hypothetical variation of the fine-structure constant alpha over cosmological
time scales. We propose a modification of the alkali doublets method which
allows us to search for variation in alpha combining far infrared and
submillimeter spectroscopic observations. This variation manifests as velocity
offsets between the observed positions of the fine-structure and
gross-structure transitions when compared to laboratory wavelengths. Here we
describe our method whose sensitivity limit to the fractional changes in alpha
is about 5*10^-7. We also demonstrate that current spectral observations of
hydrogen and [C II] 158 micron lines provide an upper limit on |Delta
alpha/alpha| < 6*10^-5 at redshifts z = 3.1 and z = 4.7.
