Olives (Olea europaea cv. Chemlali and Chetoui) used for oil production were stored, in plastic containers, at 5 °C for four different periods (0–3 weeks) before oil extraction. After storage, the oils were extracted from the fruits, and the acidity, peroxide value, coefficients of specific extinction at 232 and 270 nm, stability, pigments, total phenols, fatty acids, and volatile compounds were determined. The results showed that storage of fruits produced losses in the olive oil quality. During storage, a marked decrease in total phenols content was observed. The cultivar richer in phenols (862.16 mg kg−1 in Chétoui) had a lower loss (25%). On the contrary, in Chemlali olive oil, the starting value of 728.52 mg kg−1 decreased to 469.25 mg kg−1, with a loss of 35%. Chétoui and Chemlali olive oils presented the highest oxidative stability before storage (58.76 and 47.05 h, respectively), while the lowest values were recorded using olives stored for 3 weeks (54.46 and 43.43 h, respectively). The changes in the volatile bouquet were determined using headspace solid phase microextraction (HS-SPME). Thirty compounds were characterised by GC–FID and GC–MS. Compounds belonging mainly to alcohols, esters, aldehydes, ketones and hydrocarbons chemical classes characterised the volatile profiles.