We investigate the instability of a tubular fluid membrane made of a water-
soluble surfactant. The tubules are obtained at high brine salinities. The
instability is due to introduction within the vesicle multilayer of an alka
ne. We measure the wavelength of this instability versus the unperturbed ra
dius of the tubules and interpret this selection by using a model that incl
udes not only the surface tension in the elastic energy, but also the effec
t of the asymmetry induced by the oil as a spontaneous curvature. The linea
r stability analysis shows that within this model the selection is indeed d
ue to nonzero positive spontaneous curvature. [S1063-651X(98)03712-X].