Decadal climate prediction presumes there are decadal-timescale processes and mechanisms that, if initialized properly in models, potentially provide predictive skill more than one or two years into the future. Candidate mechanisms involve Pacific decadal variability and Atlantic multidecadal variability, elements of which involve slow fluctuations of tropical Pacific and Atlantic sea surface temperatures (SSTs) from positive anomalies (positive phase) to negative anomalies (negative phase). Here we use model experiments to show that there tends to be a weak opposite-sign SST response in the tropical Pacific when observed SSTs are specified in the Atlantic, while there is a weak same-sign SST response in the tropical Atlantic when observed SSTs are specified in the tropical Pacific. Net surface heat flux in the Atlantic and ocean dynamics in the Pacific play contrasting roles in the ocean response to specified SSTs in the respective basins. We propose that processes in the Pacific and Atlantic are sequentially interactive through the atmospheric Walker circulation along with contributions from midlatitude teleconnections for the Atlantic response to the Pacific.