Frying performance of olive-pomace oils (OPOs) as compared to sunflower oils (SOs) and high-oleic sunflower oils (HOSOs) was studied in discontinuous frying (DF) and continuous frying (CF) for the first time. DF is used in household, restaurants and frying outlets, while CF is used in the food industry. Oil alteration during frying was determined by measurements of polar compounds (PC) and polymers. Fried potatoes were analyzed for oil absorption and alteration, color, and evaluated in an acceptability test. Results for DF showed that all SOs reached 25% PC at the 9th frying operation (FO), whereas HOSOs did between the 17–18th FO and variable results were found for OPOs since initial levels of diacylglycerols were different. Rates of formation of PC or polymers were the lowest for OPOs, thus showing the best performance in DF. Specifically for PC, relative rates of formation were 1.00–1.11, 2.46–2.71 and 1.37–1.41 for OPOs, SOs and HOSOs respectively. In CF, OPOs and HOSOs behaved similarly and better than SOs, although none reached 25% PC after 40 FO. The good performance of OPOs can be attributed to the high monounsaturated-to-polyunsaturated ratio, in common with HOSOs, and the additional positive effect of minor compounds, especially β-sitosterol and squalene.