Owing to excited-state proton transfer in 2-naphthol solutions, the fluorescence excitation–emission matrices (EEMs) have factors that are highly dependent in three modes. For the first time such EEMs are used to compare the capability of PARALIND (PARAFAC with linear dependence) and conventional PARAFAC in modeling three-way EEMs having linearly dependent factors in three modes. Two primary conclusions have been drawn. First, the results indicate that a 3-factor PARAFAC model fit the data better than two PARALIND models (type 1 and 2) in this case while equally well with a specially PARALIND model (type 3); second, a negative core consistency (CC) in the 3-factor PARAFAC model is reported but the type 3 PARALIND model reports a nearly 100 CC. This work has demonstrated that a properly constrained PARALIND can fit the very special EEMs of 2-naphthol. The presence of negative CC associated with a perfect PARAFAC model would imply the presence of very special linear dependences in EEMs, which would be used as an “alarm” for the investigators to interpret the data more carefully when dealing with complicated environmental EEMs in the absence of a priori knowledge. Copyright © 2010 John Wiley & Sons, Ltd.