High-precision major, minor and trace element analyses for 44 elements have been made of 329 Late Variscan granitic and rhyolitic rocks from the Erzgebirge metallogenic province of Germany. The intrusive histories of some of these granites are not completely understood and exposures of rock are not adequate to resolve relationships between what apparently are different plutons. Therefore, it is necessary to turn to chemical analyses to decipher the evolution of the plutons and their relationships. A new classification of Erzgebirge plutons into five major groups of granites, based on petrologic interpretations of geochemical and mineralogical relationships (low-F biotite granites; low-F two-mica granites; high-F, high-P2O5 Li-mica granites; high-F, low-P2O5 Li-mica granites; high-F, low-P2O5 biotite granites) was tested by multivariate techniques. Canonical analyses of major elements, minor elements, trace elements and ratio variables all distinguish the groups with differing amounts of success. Univariate ANOVA's, in combination with forward-stepwise and backward-elimination canonical analyses, were used to select ten variables which were most effective in distinguishing groups. In a biplot, groups form distinct clusters roughly arranged along a quadratic path. Within groups, individual plutons tend to be arranged in patterns possibly reflecting granitic evolution. Canonical functions were used to classify samples of rhyolites of unknown association into the five groups. Another canonical analysis was based on ten elements traditionally used in petrology and which were important in the new classification of granites. Their biplot pattern is similar to that from statistically chosen variables but less effective at distinguishing the five groups of granites. This study shows that multivariate statistical techniques can provide significant insight into problems of granitic petrogenesis and may be superior to conventional procedures for petrological interpretation.