Tube bundle heat exchanger having a surrounding outer covering and at least one tube base which together define an inner space of the tube bundle heat exchanger, comprising - a tube bundle having a large number of heat exchange tubes which in a state arranged in the inner space can be flowed through by a first fluid and are optionally supported by additional metal support sheets, wherein the heat exchange tubes have integral ribs which are formed on the outer side of the tube and which extend in a helical line and which have a rib base, rib flanks and a rib tip and between the ribs a channel having a channel base is formed, - on the outer covering at least one inlet, via which a second fluid can be introduced into the inner space, and at least one outlet, via which the second fluid can be discharged from the inner space, - optionally at least one connection box which is arranged on the at least one tube base for distributing, redirecting or collecting the first fluid, wherein the at least one tube base has recesses as passage locations, wherein each recess has an inner surface, characterised in that - the heat exchange tubes at least protrude with the outer ribbing thereof into the recesses of the tube base, whereby a joint gap is formed in each case between the inner surface of a recess and the outer ribbing, which is located inside the recess, of a heat exchange tube, - in that the heat exchange tubes by means of joining material and incorporating the outer ribbing have a materially engaging connection to the tube base, which is formed only in a first part-portion, which extends from the front face of a heat exchange tube in an axial direction, of the recess by the joint gap being filled with joining material in this first part-portion so that a second part-portion, in which the joint gap is not filled with joining material, of the recess remains, wherein the heat exchange tube in the region of the second part-portion at the outer tube side further has an outer ribbing. - a tube bundle having a large number of heat exchange tubes which in a state arranged in the inner space can be flowed through by a first fluid and are optionally supported by additional metal support sheets, wherein the heat exchange tubes have integral ribs which are formed on the outer side of the tube and which extend in a helical line and which have a rib base, rib flanks and a rib tip and between the ribs a channel having a channel base is formed, - on the outer covering at least one inlet, via which a second fluid can be introduced into the inner space, and at least one outlet, via which the second fluid can be discharged from the inner space, - optionally at least one connection box which is arranged on the at least one tube base for distributing, redirecting or collecting the first fluid, wherein the at least one tube base has recesses as passage locations, wherein each recess has an inner surface, characterised in that wherein the at least one tube base has recesses as passage locations, wherein each recess has an inner surface, characterised in that - the heat exchange tubes at least protrude with the outer ribbing thereof into the recesses of the tube base, whereby a joint gap is formed in each case between the inner surface of a recess and the outer ribbing, which is located inside the recess, of a heat exchange tube, - in that the heat exchange tubes by means of joining material and incorporating the outer ribbing have a materially engaging connection to the tube base, which is formed only in a first part-portion, which extends from the front face of a heat exchange tube in an axial direction, of the recess by the joint gap being filled with joining material in this first part-portion so that a second part-portion, in which the joint gap is not filled with joining material, of the recess remains, wherein the heat exchange tube in the region of the second part-portion at the outer tube side further has an outer ribbing.