A method of processing seaweed, preferably a brown seaweed, comprises the following steps: (I) treating seaweed with an alcohol having one to six carbon atoms, preferably ethanol, to form an alcoholic fraction and an insoluble first seaweed residue; (II) separating the alcoholic fraction; (III) removing the alcohol from the alcoholic fraction to form a concentrate comprising biologically active low molecular weight compounds; (iv) extracting the first seaweed residue with an aqueous solution at a pH of less than 6 to form an aqueous first extract and an insoluble second seaweed residue; (v) optionally concentrating the first extract; and (vi) adjusting the pH of the resulting concentrated extract to a value in the range of 5 to 8 to obtain a first polysaccharide, fraction comprising a mixture of laminaran and fucoidan.