An apparatus and process for processing outer surfaces of glass containers (50) for use in pharmaceutical, medical or cosmetic applications, said glass containers (50) having a cylindrical main body (52). The process comprises: providing (S1) a plurality of containers (50); separating individual containers from said plurality of containers (50); and sequentially conveying said individual containers (50) through a processing station (1; 61). In the processing station (1; 61), the individual containers (50) are rotated about a longitudinal axis thereof while outer surfaces of the cylindrical main bodies (52) are in contact with a scrubbing member (27; 30, 35), for reducing an adhesive surface behavior of the outer surfaces of the cylindrical main bodies (52) of the individual containers. In this manner the surface properties of glass containers may be enhanced significantly with a cost-efficient and simple processing to thereby prevent undesired ‘stickiness behavior’ of the glass containers.