In order to clarify how cis- and trans-unsaturation of acyl chains influences the structure and properties of the metastable alpha-phase of triacylglycerols (TAGs), the conformation and packing of acyl chains and their temperature dependence were investigated by means of vibrational spectroscopy (IR and Raman) and powder X-ray diffractometry for typical saturated and cis- and trans-unsaturated TAGs, namely, tristearin, triolein, and trielaidin, which have clarified the following characteristics of each TAG. In the high-temperature range close to the melting point, the acyl chains form the hexagonal subcell for tristearin and trielaidin but they build the pseudohexagonal subcell for triolein. On the other hand, both cis- and trans-double bonds have a significant influence on the conformation of acyl chains. In triolein and trielaidin where the acyl chains are divided into two parts by a C=C bond, namely, the methyl-sided and the glycerol-sided chains, the glycerol-sided chain exhibits selective conformational disordering in the alpha-phase of these TAGs. The structural changes of acyl chains caused by cooling are also significantly affected by cis- and trans-unsaturation. For tristearin, the greater part of hydrocarbon segments change their packing from the hexagonal subcell to the pseudohexagonal subcell by cooling, while the greater part of hydrocarbon segments keep the hexagonal subcell structure and only the smaller part of them transform to the pseudohexagonal subcell for trielaidin. On the other hand, triolein does not exhibit any major changes with respect to subcell structure on cooling.