A method for solving various infinite medium and half-space multigroup transport problems with anisotropic transfer is presented. A set of eigensolutions for the homogeneous multigroup equations is obtained and is shown to have “full-range” completeness and orthogonality properties. These properties then can be used to solve for the infinite medium Green's function. Half-space problems are solved in two distinct steps. First, the emergent distribution is calculated. Then, application of the full-range completeness property gives the complete solution everywhere in the half-space. The success of this method implies that the eigensolutions also possess a “half-range” completeness property.