  It has long been argued that better timing precision allowed by satelites
like Rossi X-ray Timing Experiments (RXTE) will allow us to measure the orbital
eccentricity and the angle of periastron of some of the bright persistent high
mass X-ray binaries (HMXBs) and hence a possible measurement of apsidal motion
in these system. Measuring the rate of apsidal motion allows one to estimate
the apsidal motion constant of the mass losing companion star and hence allows
for the direct testing of the stellar structure models for these giant stars
present in the HMXBs. In the present paper we use the archival RXTE data of two
bright persistent sources, namely Cen X-3 and SMC X-1, to measure the very
small orbital eccentricity and the angle of periastron. We find that the small
variations in the pulse profiles of these sources rather than the intrinsic
timing accuracy provided by RXTE, limit the accuracy with which we can measure
arrival time of the pulses from these sources. This influences the accuracy
with which one can measure the orbital parameters, especially the very small
eccentricity and the angle of periastron in these sources. The observations of
SMC X-1 in the year 2000 were taken during the high flux state of the source
and we could determine the orbital eccentricity and $\omega$ using this data
set.
