A group of polysaccharides, called galactomannans I, were precipitated as their insoluble copper complexes from aqueous solutions of the crude polysaccharides obtained from each of the organisms designated in the title. The five galactomannans I were homogeneous under conditions of electrophoresis and ultracentrifugation and had high positive specific rotations. The major constituent monosaccharide was D-mannose; amounts of D-galactose ranged from nil for the polysaccharide from T. rubrum to 13% for that from T. schönleinii. Methylation and hydrolysis of the five galactomannans I yielded varying amounts of the following: 2,3,5,6-tetra-O-methyl-D-galactose (not present in the products from T. rubrum), 2,3,4,6-tetra-O-methyl-D-mannose, 2,3,4-tri-O-methyl-D-mannose, 2,4,6-tri-O-methyl-D-mannose, 3,4-di-O-methyl-D-mannose, and 3,5-di-O-methyl-D-mannose. Periodate oxidation results agreed with the methylation studies. The gross structural features of each galactomannan I appear to be the same, namely, a basic chain of 1 → 6 linked α-D-mannopyranose units for approximately every 22 of which there is a 1 → 3 linked α-D-mannopyranose residue. Branch points occur along the 1 → 6 linked chain at the C2 positions of the D-mannopyranose units and once in every 45 units at the C2 position of a 1 → 6 linked D-mannofuranose residue. The D-galactose in the polysaccharides is present exclusively as non-reducing terminal furanose units; non-reducing terminal units of D-mannopyranose are also present. The variations in the identities and relative amounts of the non-reducing terminal units were the only apparent differences in the gross structural features within this group of polysaccharides.