  We analyze the possibilities of detecting a signal in the hydrogen 21~cm
line, which was formed in the early Universe during the the Dark Ages
cosmological epoch, using the Ukrainian radio telescopes UTR-2 and GURT of the
National Academy of Sciences of Ukraine. As a result of cosmological expansion,
this line is shifted to the decameter range of wavelengths
($\lambda_{obs}\approx18$ m, $\nu_{obs}\approx16$ MHz) and is in the band of
operational frequencies of these telescopes. The brightness temperature of the
predicted sky-averaged global signal ranges from $\sim-0.08$ to $\sim0.02$ K,
depending on the cosmological model. Such a faint signal is a challenge even
for the world's largest radio telescope in the decameter wavelength range,
UTR-2, since the signal level of the foreground synchrotron radiation of the
Galaxy at these wavelengths is 20000--40000~K. The paper highlights the
peculiarities of spectroscopy at the decameter waves, interfering factors of
natural and instrumental origin and the ways of eliminating them in order to
reliably detect the signal in the 21~cm line, which can become an important
source of information both about the environment in which the first stars and
galaxies were born, and about the nature of dark matter particles and the
magnitude of primordial magnetic fields. It was concluded that the detection of
such a signal using the most sensitive radio telescopes at the decameter
wavelength range is possible (with the signal integration over the frequency
band of 25~MHz), the detection time will be $\sim50$~days) and can be
implemented in the coming years of peace in Ukraine.
