  The recent discovery of a planetary transit in the star HD 209458, and the
subsequent highly precise observation of the transit lightcurve with Hubble
Space Telescope, is encouraging to search for any phenomena that might induce
small changes in the light curve. Here we consider the effect of the quadrupole
moment of the parent star and of a possible second planet perturbing the orbit
of the transiting planet. Both of these cause a precession of the orbital plane
and of the periastron of the planet, which result in a long-term variation of
the duration and the period of the transits. For a transiting planet at 0.05
AU, either a quadrupole moment similar to that of the Sun or the gravitational
tug from an Earth-like planet on an orbit of semimajor axis ~ 0.2 AU and a
relative inclination near the optimal 45 degrees would cause a transit duration
time derivative of ~ 1 second per year.
