Based on the monthly average data of NCEP/NCAR Reanalysis, using a specially developed technique, the interannual variability of the sea level pressure (SLP) anomalies associated with the Global Atmospheric Oscillation (GAO) for the period 1950-2021 was studied. The field of mean deviations of the SLP anomalies during the El Niño – Southern Oscillation (ENSO) from the interannual GAO variability has been calculated. It is shown that the variability of the SLP anomalies during the GAO contains, in addition to the mode associated with the ENSO, also the mode of interannual climatic variability associated with the Antarctic Oscillation (AAO) – the Southern Annular Mode (SAM). It was found that the GAO does not include a part of the SLP anomaly variability associated with El Niño and La Niña events of the Central Pacific type. At all other grid nodes, the field of mean deviations of the SLP anomalies in the ENSO from the GAO has SLP differences slightly different from zero and formally statistically insignificant. This means that in the interannual climatic variability of the SLP associated with the GAO, there are only two modes: ENSO and SAM. With the help of cross-wavelet analysis, the relationships between the ENSO and SAM indices were studied. Negative relationships were found between these indices on fluctuation periods of about 11 years. An analysis of the time series of these indices and the time series of total solar irradiance (TSI) made it possible to put forward a hypothesis about the influence of synchronization and desynchronization of quasi-11-year changes in solar activity and ENSO on the weakening and strengthening of negative relationships between ENSO and SAM at periods of oscillations of about 11 years.