Abstract: The present invention relates to the field of human and animal nutrition, and in particular to certain novel compositions of conjugated linoleic acids (CLA). In particular, the present invention relates certain isomers of conjugated linoleic acids at either the SN1 and SN3 or SN2 positions of the acylglyceride molecule and another fatty acyl residue at the other of the SN1 and SN3 or SN2 positions of the acylglyceride molecule. These novel acylglyceride compositions containing conjugated linoleic acyl residues, medium chain fatty acyl residues, long chain fatty acyl residues, and ?3, ?6, and ?9 fatty acyl residues are efficacious as pharmaceutical compositions, animal feed additives, and human dietary supplements.