Interannual variations of atmospheric CO2 concentrations at Mauna Loa are almost masked by the seasonal cycle and a strong trend; at the South Pole, the seasonal cycle is small and is almost lost in the trend and interannual variations. Singular-spectrum analysis (SSA) issued here to isolate and reconstruct interannual signals at both sites and to visualize recent decadal changes in the amplitude and phase of the seasonal cycle. Analysis of the Mauna Loa CO2 series illustrates a hastening of the CO2 seasonal cycle, a close temporal relation between Northern Hemisphere (NH) mean temperature trends and the amplitude of the seasonal CO2 cycle, and tentative ties between the latter and seasonality changes in temperature over the NH continents. Variations of the seasonal CO2 cycle at the South Pole differ from those at Mauna Loa: it is phase changes of the seasonal cycle at the South Pole, rather than amplitude changes, that parallel hemispheric and global temperature trends. The seasonal CO2 cycles exhibit earlier occurrences of the seasons by 7 days at Mauna Loa and 18 days at the South Pole. Interannual CO2 variations are shared at the two locations, appear to respond to tropical processes, and can be decomposed mostly into two periodicities, around (3 years)-1 and (4 years)-1, respectively. Joint SSA analyses of CO2 concentrations and tropical climate indices isolate a shared mode with a quasi-triennial (QT) period in which the CO2 and sea-surface temperature (SST) participation are in phase opposition. The other shared mode has a quasi-quadrennial (QQ) period and CO2 variations are in phase with the corresponding tropical SST variations throughout the tropics. Together these interannual modes exhibit a mean lag between tropical SSTs and CO2 variations of about 6-8 months, with SST leading. Analysis of the QT and QQ signals in global gridded SSTs, joint SSA of CO2 and ??13C isotopic ratios, and SSA of CO2 and NH-land temperatures indicate that the QT variations in CO2 mostly reflect upwelling variations in the eastern tropical Pacific. QQ variations are dominated by the CO2 signature of terrestrial-ecosystem response to global QQ climate variations. Climate variations associated with these two interannual components of tropical variability have very different effects on global climate and, especially, on terrestrial ecosystems and the carbon cycle.