A method and apparatus are set forth for transferring a cryogenic fluid. A polymeric, coaxial (i.e. “tube-in-tube” geometry) transfer line is utilized where a first portion of the cryogenic fluid flows through the inner tube while a second portion flows through an annulus between the inner tube and outer tube which annulus is at a lower pressure than the inside tube. In one embodiment, the inner tube is substantially non-porous and the transfer line is preceded by a flow control means to distribute at least part of the first and second portions of the cryogenic fluid to the inner tube and annulus respectively. In a second embodiment, the inner tube is porous with respect to both gas permeation and liquid permeation such that both a gaseous part and a liquid part of the first portion permeates into the annulus to form at least a part of the second portion.