A method for generating an immune response in a vertebrate, the method comprising administering to the vertebrate an immunomer comprising at least two oligonucleotides linked at their 3′ ends or internucleotide linkages or a functionalized nucleobase or sugar to a non-nucleotidic linker, wherein at least one of the oligonucleotides is an immunostimulatory oligonucleotide having an accessible 5′ end and comprising an immunostimulatory dinucleotide selected from the group consisting of C*pG, CpG* and C*pG*, wherein C is cytidine or 2′-deoxycytidine, C* is 2′deoxythymidine, arabinocytidine, 2′-deoxy-2′-substituted-arabinocytidine, 2′-O-substituted-arabinocytidine, 2′-deoxy-5-hydroxycytidine, 2′-deoxy-N4-alkyl-cytidine, 2′-deoxy-4-thiouridine or other non-natural pyrimidine nucleoside, G is guanosine or 2′-deoxyguanosine, G* is 2′-deoxy-7-deazaguanosine, 2′-deoxy-6-thioguanosine, arabinoguanosine, 2′-deoxy-2′-substituted-arabinoguanosine, 2′-O-substituted-arabinoguanosine, or other non-natural purine nucleoside, and p is an internucleoside linkage selected from the group consisting of phosphodiester, phosphorothioate, and phosphorodithioate.