This invention involves a type of oligosacoharides and its their sulfate derivatives. The backbone of the oligosaccharides consists of 4 to 14 glucose residues, while the side chains contain 0 to 4 glucose residues. There are at least one 1->3.alpha. linkage and .beta.-(1->3)-Iinkage or .beta.-(1->4) linkage in the backbone. These oligosaccharides, and their sulfates have immune enhancing, antitumor, and antiviral activities. They can be used in immune enhancing, antitumor, and antiviral medicine compounds that would be used as therapeutic treatments.