The cell-wall structure of the red alga Rhodymenia palmata has been examined by the methods of X-ray diffraction analysis and electron microscopy, including ultra-thin sectioning. The cell wall is shown to consist of numerous lamellae each of which is made up of unoriented, crystalline microfibrils embedded in an amorphous matrix of other cell-wall constituents. The material can be stretched reversibly up to 100% when wet, and the stretching induces orientation of the microfibrils. The '$\alpha $ cellulose' fraction, which accounts for only 2 to 7% of the original dry weight, was isolated chemically and was analyzed by means of hydrolysis and paper chromatographic separation of the resulting sugars, and it was found to be composed of approximately equal quantities of glucose and xylose residues. Chemical treatment of the cell wall was found to cause considerable variations in the X-ray diagrams, which are discussed. It is concluded that the microfibrils contain both glucose and xylose residues in approximately equal proportions and that chemical treatment in this case causes changes in crystallinity of the structural component of the wall. The importance of these findings for the meaning of the term cellulose is discussed. The X-ray diagram of older fronds was found to be complicated by the occurrence of extra rings due to the presence of floridean starch, and the highly elastic properties of the thallus enabled the diagrams of the starch and the cell wall to be separated.