In this thesis we investigate coupling and preconditioning techniques for 19D hybrid neutronics calculations. Each problem is represented by two spatial regions with Sn in one region and either Diffusion (P1) or P3 in the other region. For each of these two cases we define one coupling scheme and two different preconditioned systems. These systems are solved with both fixed9point iteration and the GMRES Krylov method. The solution techniques are compared in terms of iteration count and computational cost. Preconditioning with a global diffusion operator is found to be very effective for the most difficult problems.