Space-time evolution of the dominant El Ni¿o--Southern Oscillation (ENSO) signal in the tropical eastern Pacific-Atlantic domain is investigated (1979--2004). Multi-Taper-Method, Singular Value Decomposition (MTM/SVD) and complex empirical orthogonal functions (CEOF) are applied to four variables: sea surface temperature (SST), upper ocean heat storage (HST), zonal surface wind (ZSW), and sea level pressure (SLP). Anomalous evolution for all variables find a dominant ENSO signal (3.4--5.7 years band period) composed of mixed standing modes and propagating modes. The latter evolve eastward from the eastern Pacific Ocean, into the tropical Atlantic basin at ~20 cm s-1. As such, peak signals in the equatorial Atlantic lag that in the eastern equatorial Pacific by ~12--18 months. The slow SST/SLP coupled wave propagating through the Caribbean Sea resembles the global ENSO wave identified by White and Cayan (2000).