A theory of the O-16 --> O-18 isotope effect in the manganites is developed
. It is based on the facts that an excess in the oxygen content is a thermo
dynamic necessity, and that it is isotope-dependent. As the excess oxygen a
cts as an acceptor, the charge-carrier density is isotope-dependent. On the
other hand, the excess oxygen creates an internal pressure in the crystal
which is also isotope-dependent. Using a realistic model for the manganites
and accounting for the phonon contribution, one obtains excellent agreemen
t with experiment and predicts the inversion of the isotope effect at eleva
ted temperatures. The former fact makes it possible to discard the assumpti
on that the electron-phonon coupling in the manganites is anomalously stron
g.