We investigate, using quasi-elastic light scattering, some features of the long-wavelength, low-frequency modes of the hexagonal phase often encountered in the study of lyotropic (surfactant-solvent) systems. The hexagonal phase is swollen by an oil-based ferrofluid, allowing magnetically aligned samples to be prepared. We show experimentally the anisotropy of the two lowest-frequency modes. We develop a model which predicts that these slow modes are associated to particle diffusion and tube motion. With the help of microscopic as well as phenomenological analyses, we suggest that the latter presumably corresponds to a peristaltic mode. Confinement effects on the one-dimensional, Brownian diffusion of the colloids along the tube axis together with the coupling between the two modes are studied experimentally, varying the tube diameter to particle size ratio.