  Context. Radial velocity monitoring of very cool dwarfs such as late M- and
hot L-dwarfs has become a promising tool to search for rocky planets as well as
to follow-up planetary candidates around dwarfs found by transit surveys. These
stars are faint at optical wavelengths, as their spectral flux distribution
peaks at near-infrared (NIR) wavelengths. For this reason, it is desirable to
measure the radial velocities in this wavelength regime. However, in the NIR
there are only very few medium- and high-resolution spectrographs available
which are mounted at large telescopes. In the near future, high-resolution
spectrographs for the NIR will be built, which will allow us to search for
rocky planets around cool M-dwarfs and L-dwarfs from radial velocities
monitoring.
  Methods. Stellar atmosphere synthetic models for an M- and an L-dwarf with
temperatures of 2200 K and 1800 K, respectively, and a theoretical spectrum of
the Earth's transmission in the spectral range from 0.9 to 2.5 \mum are used.
We simulate a series of Doppler-shifted spectra observed with different
resolving powers and signal-to-noise ratios, and for different rotational
broadenings of the dwarf. For different combinations of the input parameters we
recover the radial velocity by means of cross-correlation with a high
signal-to-noise ratio template and determine the associate uncertainties.
  Results. The highest precision in radial velocity measurements for the cool
M-dwarf is found in the Y band around 1.0 \mum, while for the L-dwarf it is
determined in the J band around 1.25 \mum. We note that synthetic models may
lack of some faint absorption features or underestimate their abundances.
Conversely, some instrumental/calibration aspects that are not taken into
account in our estimations would rise the uncertainties.
