A process for producing a heat exchanger tube (1) with a highly porous surface structure, in particular for evaporating liquids from pure substances or mixtures on the outside of the tube. The process starts from a rolling operation, by means of which helical fins (2) are produced on the outside of the tube, which fins, in turn, are deformed in a plurality of compression steps by means of gearwheel-like compression wheels (6, 7) in such a manner that the projections (12a, 12b) formed in each case form a cover (3a) for the passages (3) which are situated between the fins (2). The high level of porosity is achieved as a result of the remaining pores (13) and/or slots (14).