  The method of geodesic deviations provides analytic approximations to
geodesics in arbitrary background space-times. As such the method is a useful
tool in many practical situations. In this note we point out some subtleties in
the application of the method related to secular motions, in first as well as
in higher order. In particular we work out the general second-order
contribution to bound orbits in Schwarzschild space-time and show that it
provides very good analytical results all the way up to the innermost stable
circular orbit.
