The ability of reversed-phase high-performance liquid chromatography (RP-HPLC) to separate some positionally isomeric disaturated and monounsaturated triacylglycerols (TAGs) as intact species is demonstrated for the first time. Mobile phases of acetonitrile modified with methanol, ethanol, 2-propanol, 1-propanol, 1-butanol, acetone, or dichloromethane were tested for the separation of POP-PPO, PLP-PPL, PEP-PPE, and PDP-PPD (P-palmitic, O-oleic, L-linoleic, E-eicosapentaenoic, D-docosahexaenoic acid residue) on a single RP-HPLC column. The resolution improved with increasing number of double bonds in the acyl residues. While POP and PPO were only partially resolved, PDP and PPD were fully separated with all tested mobile phases, except those containing methanol. Also separated were the four TAGs having the same equivalent carbon number (ECN = 42), PEP, PPE, PDP, and PPD, on a single RP-HPLC column with mobile phase acetonitrile-2-propanol (70:30, v/v) at 0.8 mL/min. In all cases the isomer with the unsaturated acyl residue in either 1- or 3-position was retained more strongly than the respective 2-isomer.