The production of microstructured surfaces in magnesium alloys, containing zinc as the major alloying element, in particular in absorbable implants such as stents, wherein microstructures in sizes of up to 5 μm (micrometers) are generated on a magnesium alloy base body of the absorbable implant, for example of the absorbable stent, by way of optionally combined, pickling and electrochemical micropolishing processes, and allow better adhesion of a polymer coating (including higher break resistance) and higher corrosion resistance. The microstructured surface is produced out of the bulk material and exhibits no delamination from the base material during the mechanical deformation of the implant.