Several studies have reported evidence of interference between respiratory viruses: respiratory viruses rarely reach their epidemic peak concurrently and there appears to be a negative association between infection with one respiratory virus and co-infection with another. We used results spanning 16 years (2002–2017) of a routine diagnostic multiplex panel that tests for nine respiratory viruses to further investigate these interactions in Victoria, Australia. Time series analyses were used to plot the proportion positive for each virus. The seasonality of all viruses included was compared with respiratory syncytial virus (RSV) and influenza A virus using cross-correlations. Logistic regression was used to explore the likelihood of co-infection with one virus given infection with another. Seasonal peaks were observed each year for influenza A and RSV and less frequently for influenza B, coronavirus and parainfluenza virus. RSV circulated an average of 6 weeks before influenza A. Co-infection with another respiratory virus was less common with picornavirus, RSV or influenza A infection. Our findings provide further evidence of a temporal relationship in the circulation of respiratory viruses. A greater understanding of the interaction between respiratory viruses may enable better prediction of the timing and magnitude of respiratory virus epidemics.