Heat exchanger, - having a plurality of channel devices to be flowed through with a first fluid (F 1), which are arranged above one another in a stack-like manner along a stack direction, - wherein each channel device has a plate pair having a first and a second plate (3a, 3b), which in the stack direction delimit a first fluid channel to be flowed through by the first fluid (F 1), - wherein two channel devices adjacent in stack direction are arranged distanced to one another such that by means of an interspace formed between the two adjacent channel devices is formed a second fluid channel fluidically separated from the first fluid channel to be flowed through by a second fluid (F 2), - wherein in the first fluid channel of at least one channel device, preferably of all channel devices, is provided a plurality of channel elements which are connected both with the first and with the second plate (3a, 3b), such that the two interspaces of the channel device adjacent along the stack direction communicate fluidically with one another by means of the channel elements, - wherein the channel element is formed as a tube body, which comprises a circumferential wall partially delimiting a channel inner chamber, wherein the channel inner chamber is delimited on the end face by a first through-opening and a second through-opening located opposite thereto, characterised in that - at least the channel elements and the plate pairs of the heat exchanger are produced by means of an additive production method, - the circumferential wall of the channel element in a cross-section perpendicular to the axial direction has an elliptical geometry. - having a plurality of channel devices to be flowed through with a first fluid (F 1), which are arranged above one another in a stack-like manner along a stack direction, - wherein each channel device has a plate pair having a first and a second plate (3a, 3b), which in the stack direction delimit a first fluid channel to be flowed through by the first fluid (F 1), - wherein two channel devices adjacent in stack direction are arranged distanced to one another such that by means of an interspace formed between the two adjacent channel devices is formed a second fluid channel fluidically separated from the first fluid channel to be flowed through by a second fluid (F 2), - wherein in the first fluid channel of at least one channel device, preferably of all channel devices, is provided a plurality of channel elements which are connected both with the first and with the second plate (3a, 3b), such that the two interspaces of the channel device adjacent along the stack direction communicate fluidically with one another by means of the channel elements, - wherein the channel element is formed as a tube body, which comprises a circumferential wall partially delimiting a channel inner chamber, wherein the channel inner chamber is delimited on the end face by a first through-opening and a second through-opening located opposite thereto, - at least the channel elements and the plate pairs of the heat exchanger are produced by means of an additive production method, - the circumferential wall of the channel element in a cross-section perpendicular to the axial direction has an elliptical geometry.