  The efficient numerical solution of Non-LTE multilevel transfer problems
requires the combination of highly convergent iterative schemes with fast and
accurate formal solution methods of the radiative transfer (RT) equation. This
contribution begins presenting a method for the formal solution of the RT
equation in three-dimensional (3D) media with horizontal periodic boundary
conditions. This formal solver is suitable for both, unpolarized and polarized
3D radiative transfer and it can be easily combined with the iterative schemes
for solving non-LTE multilevel transfer problems that we have developed over
the last few years. We demonstrate this by showing some schematic 3D multilevel
calculations that illustrate the physical effects of horizontal radiative
transfer. These Non-LTE calculations have been carried out with our code MUGA
3D, a 3D multilevel Non-LTE code based on the Gauss-Seidel iterative scheme
that Trujillo Bueno and Fabiani Bendicho (1995) developed for RT applications.
