We point out the existence of new effects of global spacetime expansion on
local binary systems. In addition to a possible change of orbital size, the
re is a contribution to the precession of elliptic orbits, to be added to t
he well known general relativistic effect in static spacetimes, and the ecc
entricity can change. Our model calculations are done using geodesics in a
McVittie metric, representing a localized system in an asymptotically Rober
tson-Walker spacetime; we give a few numerical estimates for that case, and
briefly comment on ways in which the model should be improved.