This paper confirms and amplifies our previous demonstration (Sanopoulou, M.; Roussis, P. P.; Petropoulos, J. H. J. Polym. Sci.: Part B: Polym. Phys. 1995, 33, 993) that suitable systematic analysis and model interpretation of various features of weight gain (and loss) kinetic data, can lead to significant unambiguous conclusions concerning the physical nature and cause(s) of non-Fickian (NF) organic vapor sorption in polymer films. The relevant NF kinetic features, the modeling approaches used to provide the requisite theoretical background for analysis of the said NF features and the conclusions which can be drawn, are discussed in some detail. We then present, with the aid of supplementary new data, a much more detailed analysis and model interpretation of NF sorption in the cellulose acetate-acetone system than was given in our previous work cited above, and discuss the implications of the results obtained with regard to current views concerning the NF behavior of polymer-penetrant systems in general.