  We explore the long-term evolution of the spin period of the High Mass X-ray
Binary (HMXB) pulsar Vela X-1 over a period of 46 yr. Our analysis indicates
nearly periodic variations in the spin period of the pulsar on time-scales of
about 5.9 yr. There is suggestion of an overall spin-down behaviour of the
pulsar though it is noticed that the source appears to stay near its
equilibrium period 283.4 s since MJD 51000, with rather erratic
spin-up/spin-down episodes around this value. Our study suggests nearly cyclic
turnover in the spin behaviour of the pulsar from spin-up to spin-down regimes
on time-scales of about 17-19 yr. To our knowledge this is the first report of
periodic variation in the spin behaviour of a wind-fed accreting pulsar. We
also observe erratic episodes of spin-up and spin-down behaviour on relatively
shorter time-scales which is a well known archetype of this wind-fed X-ray
pulsar. We investigate whether nearly periodic long-term spin period changes in
the pulsar can be explained by using known mechanisms of torque reversals in
the accretion powered neutron stars. It appears that changes in the accretion
environment of the pulsar using current ideas can probably lead to long-term
spin period changes in this X-ray pulsar.
