The intraseasonal variability of the Southern Hemisphere stratosphere and troposphere is studied using multilevel geopotential height data for nine winters (1979-87). The study uses empirical orthogonal function (EOF) analysis of unfiltered data at five tropospheric and five stratospheric levels. The four leading EOFs at all tropospheric levels exhibit the patterns previously detected at 500 mb. Study of the corresponding principal components (PCs) at each level shows that the quasi-stationary anomalies associated with the leading EOFs are equivalent barotropic and exhibit no preference for early, middle or late winter. The five leading EOFs in the stratosphere fall into two classes. The first three EOFs at all levels form the first class. This class represents anomalies that are dominated by zonal wavenumber one (wave 1), exhibit strong westward tilt with height and travel slowly eastward or remain stationary. Most cases of large, persistent PC values for this class occur in early winter. The fourth and fifth EOFs form the other class. This class represents anomalies that are dominated by wavenumber two, and tilt noticeably, but less strongly than the first class, westward with height. These anomalies tend to develop mostly in late winter and to travel eastward more rapidly. The intraseasonal variability in the stratosphere resides therewith, as expected, in structures dominated by the longest planetary waves. No systemic connections between tropospheric and stratospheric persistent anomalies are apparent in the dataset.