This study analyzes tracks of Agulhas eddies in the South Atlantic. The research is based on the product "Mesoscale Eddies in Altimeter Observations of SSH". The method of automatic eddy identification detects 54,496 eddies for 1993–2017: 28,018 cyclones and 26,478 anticyclones. We show that only anticyclones are long-lived eddies in the region. We analyze 15 tracks of the anticyclones, that have more than a 2.5-year lifetime period. We find that these eddies, crossing the South Atlantic, have an almost rectilinear motion to the northwest. Their parameters (amplitude, radius, orbital velocity, and speed of drift) change during their life, however, we do not find either an explicit dependence of the displacement on topography or attenuation of eddies over time. The zonal displacement and, accordingly, the zonal component of the displacement velocity dominate, however, in some parts of the track, the vortex displacement to the equator is comparable to their zonal displacement. We hypothesize that the main problem of the inapplicability of most analytical models for interpretation of the meridional displacement is ignoring the initial values when generating eddies. We propose an alternative theory where the evolution of the initial stage of the generation of Agulhas eddies is consistent with the directional angular emission of long Rossby waves by non-zonal currents. Based on this theory, we analyze the tracks of the long-lived eddies. The proposed interpretation allows us to explain many of the observed effects but does not reject other possible scenarios for other regions of the World Ocean.