  A timing analysis of VHE gamma-ray observations of Cen X-3 taken with the
University of Durham Mark 6 telescope was performed, using both Rayleigh and
Bayesian statistics. Data from only 1 observation produced evidence for
periodicity, in a 'soft' cut data set, with an overall chance probability <0.01
and blueshifted by 6.6ms from the nominal second harmonic of the pulse period.
We show that the disappearance of the Rayleigh peak in the fully cut data set
is consistent with a gamma-ray origin hypothesis. The second part of the paper
considers theoretical models that could explain the existing data of Cen X-3 in
high and very high energy gamma-rays. On the basis of energetics, all
reasonable options for gamma-ray production must be connected to jets emerging
from the inner accretion disc around the neutron star. One principal option is
a large scale source, with R_s~10^13-14cm, assuming effective acceleration of
electrons by shocks produced by the interaction of the jets with the dense
atmosphere of the binary. The bulk of gamma-ray features could be explained by
this model except modulations at the pulsar period, which would require a
source with R_s<10^11cm. We consider hadronic and leptonic models for the
formation of such a compact object. Both models predict the episodes of pulsed
emission may be rare, of typical duration ~few hours, and the frequency of
pulsations should be significantly shifted from the nominal frequency of the
X-ray pulsar. The opportunities to distinguish between different models using
future gamma-ray observations of this X-ray binary are discussed. (v. abridged)
