Abstract A new multiway/multivariate approach is proposed to study and model the spoilage of swordfish with time and temperature of storage through the profiles of putrescine, spermidine, histamine, tyramine, tryptamine, cadaverine, spermine, and 2‐phenylethylamine. The evolution of these biogenic amines in food is a complex process that cannot be characterized by a single parameter but by a modification of the amine profiles. An experimental strategy is designed to determine these profiles in such a way that data are structurally 3‐way. Modeling the joint evolution of the biogenic amines with a PARAFAC model which explains 97.8% of variability (CORCONDIA index equals 100%) leads to estimate the storage time, storage temperature, and biogenic amines profiles. A multiple regression (determination coefficient of 0.98) based on the loadings of the 2 factors of the time profile of the PARAFAC model enables the estimation of the storage time with an error of 0.5 days.