  The X-ray source 1E 1207.4-5209 is a compact central object in the
G296.5+10.0 supernova remnant. Its spin period of 424 ms, discovered with the
Chandra X-ray Observatory, suggests that it is a neutron star. The X-ray
spectrum of this radio-quiet pulsar shows at least two absorption lines, first
spectral features discovered in radiation from an isolated neutron star. Here
we report the results of timing analysis of Chandra and XMM-Newton observations
of this source showing a non-monotonous behavior of its period. We discuss
three hypotheses which may explain the observational result. The first one
assumes that 1E 1207.$-5209 is a glitching pulsar, with frequency jumps of
\Delta f > 5 \muHz occurring every 1-2 years. The second hypothesis explains
the deviations from a steady spin-down as due to accretion, with accretion rate
varying from \sim 10^{13} to >10^{16} g s^{-1}, from a disk possibly formed
from ejecta produced in the supernova explosion. Finally, the period variations
could be explained assuming that the pulsar is in a wide binary system with a
long period, P_orb \sim 0.2-6 yr, and a low-mass companion, M_2 < 0.3 M_\odot.
