Large-scale prevention of respiratory syncytial virus (RSV) infection may have ecological consequences for co-circulating pathogens, including influenza. We assessed if and for how long RSV infection alters the risk for subsequent influenza infection. We analysed a prospective longitudinal cohort study conducted in South Africa between 2016 and 2018. For participating households, nasopharyngeal samples were taken twice weekly, irrespective of symptoms, across three respiratory virus seasons, and real-time polymerase chain reaction (PCR) was used to identify infection with RSV and/or influenza. We fitted an individual-level hidden markov transmission model in order to estimate RSV and influenza infection rates and their interdependence. Of a total of 122113 samples collected, 1265 (1.0%) were positive for influenza and 1002 (0.8%) positive for RSV, with 15 (0.01%) samples from 12 individuals positive for both influenza and RSV. We observed 2.25-fold higher incidence of co-infection than expected if assuming infections were unrelated. We estimated that infection with influenza is 2.13 (95% CI 0.97 - 4.69) times more likely when already infected with, and for a week following, RSV infection, adjusted for age. This equates to 1.4% of influenza infections that may be attributable to RSV in this population. Due to the local seasonality (RSV season precedes the influenza season), we were unable to estimate changes in RSV infection risk following influenza infection. RSV infection was associated with an increased risk for influenza infection for a short period after infection. However, the impact on population-level transmission dynamics of this individual-level synergistic effect was not measurable in this setting.