The/3-phase crystal structures of unsaturated triacylglycerols (TAGs) have been analyzed. Long spacings and melting points of monounsaturated TAGs such as 16" O. 16 and 16.0" 18 indicate a fi-3C packing mode with a methyl terrace that differs from that of the saturated /3-3 TAGs. In addition to the hydrocarbon chain subcell packing and the methyl terrace structure, the conformation of the oleoyl chain also has to be considered. This conformation is analyzed in connection with the symmetry relation between the two half-layers on either side of the plane through the double bonds. Geometric analysis shows four possibilities, which have been explored further by means of energy minimization computations. In these calculations the structure of the oleoyl chain, in its crystalline environment, has been optimized while taking all relevant intramolecular and intermolecular forces into account. Though the calculations reveal relatively small energy differences between the four possibilities, the most likely structure can still be identified. On the basis of the results obtained for the monounsaturated TAGs, proposals for the crystal structures of diunsaturated (e.g., 0 9 18. O) and triunsaturated (e.g., 0" 0" O) TAGs are briefly outlined.