This paper explores the three-way interactions between the Indian monsoon, the North Atlantic and the Tropical Pacific. Four climate records were analyzed: the monsoon rainfall in two Indian regions, the Southern Oscillation Index for the Tropical Pacific, and the NAO index for the North Atlantic. The individual records exhibit highly significant oscillatory modes with spectral peaks at 7–8 yr and in the quasi-biennial and quasi-quadrennial bands. The interactions between the three regions were investigated in the light of the synchronization theory of chaotic oscillators. The theory was applied here by combining multichannel singular-spectrum analysis (M-SSA) with a recently introduced varimax rotation of the M-SSA eigenvectors. A key result is that the 7–8-yr and 2.7-yr oscillatory modes in all three regions are synchronized, at least in part. The energy-ratio analysis, as well as time-lag results, suggest that the NAO plays a leading role in the 7–8-yr mode. It was found therewith that the South Asian monsoon is not slaved to forcing from the equatorial Pacific, although it does interact strongly with it. The time-lag analysis pinpointed this to be the case in particular for the quasi-biennial oscillatory modes. Overall, these results confirm that the approach of synchronized oscillators, combined with varimax-rotated M-SSA, is a powerful tool in studying teleconnections between regional climate modes and that it helps identify the mechanisms that operate in various frequency bands. This approach should be readily applicable to ocean modes of variability and to the problems of air-sea interaction as well.