  The orbital motion of a neutron star about its optical companion presents a
window through which to study the orbital parameters of that binary system.
This has been used extensively in the Milky Way to calculate these parameters
for several high-mass X-ray binaries. Using several years of RXTE PCA data, we
derive the orbital parameters of four Be/X-ray binary systems in the SMC,
increasing the number of systems with orbital solutions by a factor of three.
We find one new orbital period, confirm a second and discuss the parameters
with comparison to the Galactic systems. Despite the low metallicity in the
SMC, these binary systems sit amongst the Galactic distribution of orbital
periods and eccentricities, suggesting that metallicity may not play an
important role in the evolution of high-mass X-ray binary systems. A plot of
orbital period against eccentricity shows that the supergiant, Be and low
eccentricity OB transient systems occupy separate regions of the parameter
space; akin to the separated regions on the Corbet diagram. Using a Spearman's
rank correlation test, we also find a possible correlation between the two
parameters. The mass functions, inclinations and orbital semimajor axes are
derived for the SMC systems based on the binary parameters and the spectral
classification of the optical counterpart. As a by-product of our work, we
present a catalogue of the orbital parameters for every high-mass X-ray binary
in the Galaxy and Magellanic Clouds for which they are known.
