The competitive interaction with DNA of daunorubicin (DR), being present in the clinical anti-tumor drug daunoblastina, and the fluorescence probe ethidium bromide (EB) has been studied by parallel-factor analysis (PARAFAC) and full-rank parallel-factor analysis (FRA-PARAFAC) of a fluorescence excitation-emission three-way data array. The PARAFAC algorithm can furnish stable resolution results for the data array studied, if the estimated number of chemical components is consistent with the real number. The FRA-PARAFAC algorithm is not sensitive to the estimated number of components of the fluorescence data array if the estimated number is not less than the real number. Both algorithms gave identical resolution for the three components concerned DR, EB, and the complex EB-DNA. Variations of the equilibrium concentrations of free DR, EB, and the complex EB-DNA were resolved by both algorithms. Experimental observation confirms the hypothesis that DR is an intercalator of DNA and that the binding interactions of DR and EB with DNA are a pair of parallel competitive intercalation reactions on same base sites of DNA. The method exemplified by this study provides a useful approach for studying competitive interactions of different drugs with DNA in the presence of interferents.