The cross-correlation and spectral density functions of the adsorbate
density fluctuations have been calculated at the transition temperatur
e of a second order phase transition. Comparison with hydrodynamic flu
ctuations was made. Our calculations showed that for t = 0 the cross-c
orrelation functions of the critical fluctuations are positive for any
distance between the probed regions (they decay with distance as x-1/
4). The hydrodynamic cross-correlation functions for t = 0 are positiv
e when the probed regions overlap and are zero when they are separated
. The spectral density for the critical fluctuations reveals faster de
cay for low frequencies in comparison with the hydrodynamic one.