*Abstract. *For the solution of convection-diffusion problems we presenta multilevel self-adaptive mesh-refinement algorithm to resolve locallystrong varying behavior, like boundary and interior layers. The methodis based on discontinuous Galerkin (Baumann-Oden DG) discretization.The recursive mesh-adaptation is interwoven with the multigrid solver.The solver is based on multigrid V-cycles with damped block-Jacobirelaxation as a smoother. Grid transfer operators are chosen in agreementwith the Galerkin structure of the discretization, and local gridrefinementis taken care of by the transfer of local truncation errorsbetween overlapping parts of the grid.We propose an error indicator based on the comparison of the discretesolution on the finest grid and its restriction to the next coarser grid. Itrefines in regions, where this difference is too large. Several results ofnumerical experiments are presented which illustrate the performance ofthe method.