The possibility of simultaneously determining seven concerned heavy polycyclic aromatic hydrocarbons (PAHs) of the US-EPA priority pollutant list, in extra virgin olive and sunflower oils was examined using unfolded partial least-squares with residual bilinearization (U-PLS/RBL) and parallel factor analysis (PARAFAC). Both of these methods were applied to fluorescence excitation emission matrices. The compounds studied were benzo[a]anthracene, benzo[b]fluoranthene, benzo[k]fluoranthene, benzo[a]pyrene, dibenz[a,h]anthracene, benzo[g,h,i]perylene and indeno[1,2,3-c,d]-pyrene. The analysis was performed using fluorescence spectroscopy after a microwave assisted liquid-liquid extraction and solid-phase extraction on silica. The U-PLS/RBL algorithm exhibited the best performance for resolving the heavy PAH mixture in the presence of both the highly complex oil matrix and other unpredicted PAHs of the US-EPA list. The obtained limit of detection for the proposed method ranged from 0.07 to 2 μg kg(-1). The predicted U-PLS/RBL concentrations were satisfactorily compared with those obtained using high-performance liquid chromatography with fluorescence detection. A simple analysis with a considerable reduction in time and solvent consumption in comparison with chromatography are the principal advantages of the proposed method.