Two theories on the mechanism of the thickening of chain-folding lamellae occurring during isothermal crystallization are conflicting. One attributes the thickening to an annealing process by which isothermal crystallization should be accompanied. An alternative explanation proposed by the author in the preceding paper, was that the effect should be due to molecular fractionation during crystallization. In order to clarify which of the two conflicting theories is preferable, x-ray long spacings were measured for carefully fractionated polyethylene samples crystallized isothermally and quenched after varying time intervals. In contrast with the previous observation made by Hoffman and Weeks at the crystallization temperature, much less thickening was observed for these samples as compared with the unfractionated polymer (Marlex-50). The effect of crystallization temperature on the thickening behaviour was also examined. Again in favour of the fractionation theory the total amount of the thickening observed decreased remarkably with the decreasing temperature. Further, according to the above two theories the distribution of the fold lengths in the crystals formed was calculated as a function of time for the crystallization of the Marlex-50 polymer. Comparing the results of the calculations with experimental data obtained so far, it has been pointed out that the experimental results afford an evidence in favour of the fractionation theory. A possible effect of an amorphous surface layer on the individual lamella on the observed long spacing increase is also discussed briefly. © 1969 Dr. Dietrich Steinkopff Verlag.