  The improvement in observational facilities requires refining the modelling
of the geometrical structures of astrophysical objects. Nevertheless, for
complex problems such as line overlap in molecules showing hyperfine structure,
a detailed analysis still requires a large amount of computing time and thus,
misinterpretation cannot be dismissed due to an undersampling of the whole
space of parameters. We extend the discussion of the implementation of the
Gauss--Seidel algorithm in spherical geometry and include the case of hyperfine
line overlap. We first review the basics of the short characteristics method
that is used to solve the radiative transfer equations. Details are given on
the determination of the Lambda operator in spherical geometry. The
Gauss--Seidel algorithm is then described and, by analogy to the plan--parallel
case, we see how to introduce it in spherical geometry. Doing so requires some
approximations in order to keep the algorithm competitive. Finally, line
overlap effects are included. The convergence speed of the algorithm is
compared to the usual Jacobi iterative schemes. The gain in the number of
iterations is typically factors of 2 and 4 for the two implementations made of
the Gauss--Seidel algorithm. This is obtained despite the introduction of
approximations in the algorithm. A comparison of results obtained with and
without line overlaps for N2H+, HCN, and HNC shows that the J=3-2 line
intensities are significantly underestimated in models where line overlap is
neglected.
