  In this paper we address the following question: do the recent advances in
the orbit determination of the major natural satellites of Saturn obtained with
the analysis of the first data sets from the Cassini mission allow to detect
the general relativistic gravitoelectric orbital precessions of such moons? The
answer is still negative. The present-day down-track accuracy would be adequate
for Mimas, Enceladus, Thetys, Dione, Rhea and Titan and inadequate for
Hyperion, Iapetus and Phoebe. Instead, the size of the systematic errors
induced by the mismodelling in the key parameters of the Saturnian
gravitational field like the even zonal harmonics Jl are larger than the
relativistic down-track shifts by about one order of magnitude, mainly for the
inner satellites like Mimas, Enceladus, Thetys, Dione, Rhea, Titan and
Hyperion. Iapetus and Phoebe are not sensibly affected by such kind of
perturbations. Moreover, the bias due to the uncertainty in Saturn's GM is
larger than the relativistic down-track effects for all such moons. Proposed
linear combinations of the satellites' orbital elements would allow to cancel
out the impact of the mismodelling in the low-degree even zonal harmonics and
GM, but the combined down-track errors would be larger than the combined
relativistic signature.
