The binary mixture sodium decylsulphate/water exhibits a hexagonal structure for a degree of hydration of about 50 per cent by weight. In this structure the amphiphiles build infinitely long cylinders which are organized on a 2D lattice of space group p6m. If, in such a mixture, sodium decylsulphate is progressively substituted by decanol, the hexagonal structure transforms itself successively into two rectangular structures. In these rectangular structures the amphiphiles also build cylinders, but these are organized on 2D lattices with space groups cmm and pgg, respectively. This evolution of cylindrical structures in the ternary mixture is also marked by a growth of the mean normal section of the cylinders. An analysis of these results is proposed, in which the growth is accompanied by a change in the normal section, from circular for the hexagonal structure to non-circular for the rectangular structures; this change occurs abruptly at the hexagonal-rectangular transition and is stabilized by an important fluctuation of the relative concentrations of the two amphiphiles within the cylinders.