Oligonucleotides containing the non-palindromic sequence motif: X.sub.1X.sub.2X.sub.3X.sub.4X.sub.5X.sub.6X.sub.7X.sub.8, wherein X.sub.1 is C,T,G or A (preferably T or C); wherein X.sub.2 is C,T,G or A; wherein X.sub.7 is C,T,G or A (preferably G); at least three, and preferably all, of X.sub.3, X.sub.4, X.sub.5, X.sub.6 and X.sub.8 are T; and with the proviso that, in the motif, a C does not precede a G (in other terms, the nucleic acid motif does not consist of a CpG oligonucleotide), that modulate the immune response of animals of the order Primate, including humans, are disclosed. This immune modulation is characterized by stimulation of proliferation, differentiation, cytokine production and antibody production on B-cells and cell differentiation on plasmacytoid dendritic cells.