Background & objectives: : In the context of India's ongoing resurgence of COVID-19 (second wave since mid-February 2021, following the subsiding of the first wave in September 2020), there has been increasing speculation on the possibility of a future third wave of infection, posing a burden on the healthcare system. Using simple mathematical models of the transmission dynamics of SARS-CoV-2, this study examined the conditions under which a serious third wave could occur. Methods: : Using a deterministic, compartmental model of SARS-CoV-2 transmission, four potential mechanisms for a third wave were examined: (i) waning immunity restores previously exposed individuals to a susceptible state, (ii) emergence of a new viral variant that is capable of escaping immunity to previously circulating strains, (iii) emergence of a new viral variant that is more transmissible than the previously circulating strains, and (iv) release of current lockdowns affording fresh opportunities for transmission. Results: : Immune-mediated mechanisms (waning immunity, or viral evolution for immune escape) are unlikely to drive a severe third wave if acting on their own, unless such mechanisms lead to a complete loss of protection among those previously exposed. Likewise, a new, more transmissible variant would have to exceed a high threshold (R0>4.5) to cause a third wave on its own. However, plausible mechanisms for a third wave include: (i) a new variant that is more transmissible and at the same time capable of escaping prior immunity, and (ii) lockdowns that are highly effective in limiting transmission and subsequently released. In both cases, any third wave seems unlikely to be as severe as the second wave. Rapid scale-up of vaccination efforts could play an important role in mitigating these and future waves of the disease. Interpretation & conclusions: : This study demonstrates plausible mechanisms by which a substantial third wave could occur, while also illustrating that it is unlikely for any such resurgence to be as large as the second wave. Model projections are, however, subject to several uncertainties, and it remains important to scale up vaccination coverage to mitigate against any eventuality. Preparedness planning for any potential future wave will benefit by drawing upon the projected numbers based on the present modelling exercise.