The cell walls of a number of marine algae, namely species of Bryopsis, Caulerpa, Udotea, Halimeda and Penicillus and of one freshwater alga, Dichotomosiphon, are examined using both chemical and physical techniques. It is shown that, with the possible exception of Bryopsis, cellulose is completely absent and that the walls contain instead $\beta $-1,3-linked xylan as the structural polysaccharide. Bryopsis contains, in addition, a glucan which is most abundant in the outer layers of the wall and which stains like cellulose. The xylan is microfibrillar but the microfibrils are more strongly adherent than they are in cellulose, and in some species appear in the electron microscope to be joined by short crossed rod-like bodies. The orientation of the microfibrils is found to vary, ranging from a net tendency to transverse orientation through complete randomness to almost perfect longitudinal alinement. The microfibrils are negatively birefringent, so that all walls seen in optical section, and all parallel arrays of microfibrils whether in face view or in section (except strictly transverse section) are negatively birefringent. With Bryopsis, the negative birefringence in face view is overcompensated by the positive birefringence of the incrusting glucan so that the true birefringence of the crystalline polysaccharide is observed only after the glucan is removed. The X-ray diagram of parallel arrays of microfibrils as found, for instance, in Penicillus dumetosus shows that the xylan chains are helically coiled, in harmony with the negative birefringence. It is deduced that the microfibrils consist of hexagonally packed, double-stranded helices. The diameter of the helices increases with increasing relative humidity, as water is taken into the lattice, from 13$\cdot $7 angstrom in material dried over phosphorus pentoxide to a maximum of 1$\cdot $54 angstrom at 65% relative humidity when the xylan contains 30% of its weight as water. The repeat distance along the helix axis ranges from 5$\cdot $85 angstrom (dry) to 6$\cdot $06 angstrom (wet), the length of a half turn of each helix containing three xylose residues. The incrusting substances in these walls often include a glucan which is said also to be 1,3-linked. The significance of the extensive differences between this xylan and cellulose are examined both as regards some of the physical properties of the respective cell walls and in relation to the taxonomic position of these plants.