A pipe for forming air flow pipelines in a structure that includes a flexible tube made from composite material, the tube having, on the length of same, sections for which the wall of the tube is stiffened by means of structural elements made from a rigid composite material incorporated into the wall of the tube. The structural elements are configured and arranged at the surface of the tube in such a way as to form a lattice framework surrounding the wall of the tube. The pipe further includes electrical conductors, disposed longitudinally on the wall of the pipe, the electrical conductors having a straight path at the stiffened sections of the pipe and a meandering path at certain of the non-stiffened sections of the pipe, the meandering allowing the conductor to tolerate the possible twisting of the pipe when it is installed in the structure.