We investigate the orbital behaviour of close high mass X-ray binaries
(HMXBs), including the effects of the evolutionary growth of the mome
nt of inertia and mass loss by stellar wind from the main-sequence sta
r. We find that a nearly synchronous state implies in the context of t
idal evolution a rapid decrease of the orbital period for binary syste
ms close to the Darwin instability. In this frame, the observed orbita
l decays \P/P\greater than or equal to 10(-6) yr(-1) in the Cen X-3 an
d SMC X-1 systems appear to be characteristic of synchronous HMXBs con
taining a neutron star. The rate of change in orbital period is expect
ed to be one or two orders of magnitude smaller in close HMXBs with bl
ack hole candidates.