  The periastron shift and the Lense-Thirring effect of bound orbital motion in
a general axially symmetric space-time given by Pleba\'nski and Demia\'nski are
analyzed. We also define a measure for the conicity of the orbit and give
analytic expressions for all three observables in terms of hyperelliptic
integrals and Lauricella's $F_D$ function. For an interpretation of these
analytical expressions, we perform a post-Schwarzschild and a post-Newton
expansion of these quantities. This clearly shows the influence of the
different space-time parameters on the considered observables and allows to
characterize Kerr, Taub-NUT, Schwarzschild-de Sitter, or other space-times.
