The role of local air-sea interactions over the tropical Indian Ocean (TIO) and remote forcing from the tropical Pacific Ocean in the formation and maintenance of southern TIO Rossby waves during El Niño and positive Indian Ocean Dipole (IOD) years is investigated. These Rossby waves are significantly intensified during the El Niño and IOD cooccurrence years, as compared to those during pure El Niño or IOD years. Coupled ocean-atmosphere model sensitivity experiments reveal that air-sea coupled processes in the TIO are responsible for the Rossby wave formation and its maintenance from boreal summer to fall, while remote forcing from the Pacific intensifies and maintains these waves up to the following spring. During the cooccurrence years, the Rossby waves are generated by both the persistent equatorial easterlies and off-equatorial wind stress curl. During pure El Niño years, however, only off-equatorial wind stress curl exists to drive weak Rossby wave. Asymmetric heating associated with IOD and the mean background easterly vertical wind shear (in the northern hemisphere) during summer and fall excite two symmetric anticyclones in both sides of the equator as atmospheric Rossby wave response, which are responsible for the anomalous equatorial surface easterlies. In contrast, symmetric heat sink over the Maritime Continent in winter associated with El Niño-induced subsidence and mean easterly vertical shear (in southern hemisphere) are responsible for strong anticyclone in the southern TIO, which supports off-equatorial wind stress curl.