We consider the Kepler two-body problem in presence of the cosmological constant Λ. Contrary to the classical case, where finite solutions exist for any angular momentum of the system L, in presence of Λ finite solutions exist only in the interval 0 < L < L lim (Λ). The qualitative picture of the two-body motion is described, and critical parameters of the problem are found. Application are made to the relative motion of the Local Group and Virgo cluster.