A metal heat exchanger tube for the evaporation of liquids on the outside of the tube, having a tube axis, a tube wall, and integrally formed ribs that run circumferentially on the outside of the tube. The ribs have a rib foot, rib flanks, and a rib tip, wherein the rib foot projects substantially radially from the tube wall. A respective groove is located between every two ribs that are adjacent to one another in the axial direction. At least first, second, and third lateral material projections, which are formed from the material of the ribs, are arranged on a first, second, and third level on the rib flanks in such a way that the grooves are largely covered by all of the material projections. The first, second, and third lateral material projections are formed on levels that are in each case differently spaced apart from the tube wall in the radial direction.