[en] The solution of steady, one-dimensional half-space multigroup transport problems with degenerate anisotropic scattering is obtained for L₁ sources and incident distributions. The solution is expressed in terms of contour integrals of the resolvent operator (lambdaI-K)/sup -1/, where K is the ''separated'' transport operator. The connection between this method and the ''Case eigenfunction'' method is briefly discussed, and the half-space albedo problem is treated in detail. This problem reduces to obtaining the Wiener--Hopf factorization of the dispersion matrix, hence to solving two coupled nonlinear, nonsingular matrix integral equations