A process for enzymatic production of glyceride compositions, specifically industrially practicable production of triglycerides, including conjugated linoleic and linolenic acid triglycerides, and the compositions produced by such process. An enzymatic reaction zone is first utilized, in which a mixture of glycerol and fatty acids or fatty acid derivatives is reacted in the presence of an enzymatic catalyst to form 1,3 diglycerides. The mixture is then circulated through a second thermal rearrangement zone, maintained at a higher temperature, to promote rearrangement of the 1,3 diglycerides to 1,2 diglycerides. Triglycerides are produced by re-circulating the mixture through the enzymatic production zone.