Southern Hemisphere (SH) stratospheric variability is investigated with respect to chaotic behavior using time series from three different variables extracted from four different reanalysis products. The results are compared with the same analysis applied to the Northern Hemisphere (NH). The probability density functions (PDFs) for the SH show persistent deviations from a Gaussian distribution. The variability is given by white spectra for low frequencies, a slope of −1 for intermediate frequencies, and −3 slopes for high frequencies. Considering the time series for winter and summer separately, PDFs show a Gaussian distribution and the variability spectra change their slopes, indicating the role of the transition between winter and summer variability in shaping the time series. The correlation (D2) and the Kaplan–Yorke (DKY) dimensions are estimated. A finite value of the dimensions can be computed for each variable and data product, except for the NCEP zonal-mean zonal wind and temperature data, which violate the requirement D2 ≤ DKY, possibly owing to the presence of spurious trends and inconsistencies in the data. The value of D2 ranges between 2.6 and 3.9, while DKY ranges between 3.0 and 4.5. The results show that both D2 and DKY display large variability in their values both for different datasets and for different variables within the same dataset. The variability of the values of D2 and DKY thus leaves open the question about the existence of a low-dimensional attractor or if the finite dimensions of the system are the result of the projection of a larger attractor in a low-dimensional embedding space.