The invention relates to a process for producing thermoplastic molding materials based on acrylonitrile-styrene-acrylate copolymers (ASA) having improved surface properties, in particular an improved stability of surface quality during storage in a hot and humid environment and a reduced content of residual monomers. The invention further relates to the use of a fluidized bed dryer and/or a flow dryer in the production of thermoplastic ASA molding materials for improving surface quality and the use of a fluidized bed dryer and/or a flow dryer in the production of thermoplastic ASA molding materials for reducing the content of residual monomers. The invention further provides ASA molding materials producible by means of the process according to the invention and also moldings.