  To estimate influence of the "dark energy" on the Keplerian orbits, we solve
the general relativistic equations of motion of a test particle in the field of
a point-like mass embedded in the cosmological background formed by the
Lambda-term with realistic cosmological Robertson-Walker asymptotics at
infinity. It is found that under certain relations between three crucial
parameters of the problem--the initial radius of the orbit, Schwarzschild and
de Sitter radii--the specific secular perturbation caused by the Lambda-term
becomes significant, i.e. can reach the rate of the standard Hubble flow. This
fact is interesting both by itself and may have important consequences for the
long-term dynamics of planets and stellar binary systems.
