  In binary radio pulsars with a main-sequence star companion, the spin-induced
quadrupole moment of the companion gives rise to a precession of the binary
orbit. As a first approximation one can model the secular evolution caused by
this classical spin-orbit coupling by linear-in-time changes of the longitude
of periastron and the projected semi-major axis of the pulsar orbit. This
simple representation of the precession of the orbit neglects two important
aspects of the orbital dynamics of a binary pulsar with an oblate companion.
First, the quasiperiodic effects along the orbit, due to the anisotropic
$1/r^3$ nature of the quadrupole potential. Secondly, the long-term secular
evolution of the binary orbit which leads to an evolution of the longitude of
periastron and the projected semi-major axis which is non-linear in time.
  In this paper a simple timing formula for binary radio pulsars with a
main-sequence star companion is presented which models the short-term secular
and most of the short-term periodic effects caused by the classical spin-orbit
coupling. I also give extensions of the timing formula which account for
long-term secular changes in the binary pulsar motion. It is shown that the
short-term periodic effects are important for the timing observations of the
binary pulsar PSR B1259--63. The long-term secular effects are likely to become
important in the next few years of timing observations of the binary pulsar PSR
J0045--7319. They could help to restrict or even determine the moments of
inertia of the companion star and thus probe its internal structure.
  Finally, I reinvestigate the spin-orbit precession of the binary pulsar PSR
J0045--7319 since the analysis given in the literature is based on an incorrect
expression for the precession of the longitude of periastron.
