  In transiting planetary systems, the angle between the orbital angular
momentum and the stellar spin is usually constrained through the
Rossiter-McLaughlin effect observed in radial velocity and can be subject to
large uncertainties, especially for hot stars (T_eff > 6250 K). It is thus
interesting to have an alternative method to constrain the value of the
obliquity and to detect companions that might have disturbed the orbit of the
planet. We show how the long-term variations in the transit duration (TDV) can
be used to constrain the obliquity of the stellar rotation axis. We introduce a
simple theory to express the secular variations in the orbital elements and
their effects on the TDVs with a general formulation valid for both oblique and
eccentric systems. Parameters or orbital elements that cannot be directly
measured, such as the longitude of the ascending node of the orbit, are avoided
thus allowing us a straightforward application. We compute the expected TDVs
for the presently known transiting systems, adopting their parameters found in
the literature. Considering the capabilities of the present or next generation
space-borne telescopes, we point out the systems that could be readily observed
and discuss the constraints derivable on their fundamental parameters. TDVs can
be used to constrain the obliquity of the stars (and possibly of the planets in
systems younger than 10 -- 100 Myr), giving information about the formation
scenarios, the strength of the tidal coupling, and the internal structure of
both the stars and the planets. Moreover, they can provide an indirect
indication of the presence of other bodies, even with a mass comparable with
that of the Earth, because they give rise to additional contributions to the
nodal precession.
