The invention provides a process for producing 2-monoglycerides (2-MG) or triglycerides (TG), particularly triglycerides having polyunsaturated fatty acid (PUFA) residues in the sn-2 positions, at an extremely high purity and a high efficiency.The 2-MG is produced by conducting alcoholysis of a starting TG with a first 1,3-lipase. Then, the TG is produced by introducing fatty acid residues to the 1- and 3-positions of the produced 2-MG by using a second 1,3-lipase. The fatty acid residue in the 2-posiiton is preferably a residue of DHA, EPA or ARA. The “first lipase” refers to one which is selective for the 1- and 3-positions and can act even on a long-chain fatty acid in alcoholysis, while the “second lipase” refers to one which is selective for the 1- and 3-positions and can produce a TG through the reaction of a 2-MG with a fatty acid ester or a free fatty acid.