The Stabilized March Technique, SMT, is extended to the numerical solution of second-order, inhomogeneous problems, i.e., the multigroup neutron diffusion equations in one space dimension, and the one-velocity neutron transport equation in one space dimension. In the SMT, the solution vector is expanded in a complete set of vectors which is used in an unstable difference equation. The error growth is controlled, however, by periodic matrix transformations and may be preset. The method has its greatest advantage in relation to the computational speed of conventional methods in elongated meshes, such as multigroup diffusion calculations, or low-order discrete ordinate or PN calculations with many spatial mesh points.