Abstract A multilevel iterative method for solving multigroup neutron transport k-eigenvalue problems in two-dimensional geometry is developed. This method is based on a system of group low-order quasidiffusion (LOQD) equations defined on a sequence of coarsening energy grids. The spatial discretization of the LOQD equations uses compensation terms which make it consistent with a high-order transport scheme on a given spatial grid. Different multigrid algorithms are applied to solve the multilevel system of group LOQD equations on grids in energy. The eigenvalue is evaluated from the LOQD problem on a coarsest grid. To further improve the efficiency of iterative schemes hybrid multigrid algorithms are developed. The numerical results of tests with a large number groups are presented to demonstrate performance of the proposed iterative schemes.