Results are presented from Principal Components Analysis of three data matrices (pollen concentration per c.c., percentages of total pollen, and analyses for eight or nine chemical elements) of c. thirty samples from each of two profiles of lake sediment of Late-Devensian age (15000 to 10000 years B.P.) from the Lake District and N.W. Scotland. The groupings of samples by their scores on the first two components of these Principal Components Analyses have been shown to produce similar divisions (zonations) to those originally produced subjectively by inspection of the percentage pollen diagrams. Though neither profile includes the classical Late-Weichselian oscillation of pollen zones I, II and III, involving expansion of percentages of birch pollen within biogenic sediment between two minerogenic layers, numerical analysis has revealed in the data from both sites a pattern involving a threefold division with revertence, and another pattern of twofold division. The subjective zonation of the percentage diagrams clearly involved a process of mental integration of these two patterns. A plot of the scores of the samples on the first two components of the Principal Components Analyses groups the samples into clusters corresponding with the zones determined by inspection; similar results are obtained for each of the three Principal Components Analyses. This is interpreted as indicative of a close relationship between pollen and chemical data which can most readily be explained on the hypothesis that the boundaries of pollen zones represent the results of environmental changes which simultaneously affected soils and vegetation.