Multicomponent cyclicity in influenza (flu) incidence had been observed in various countries (e.g. periods T = 1, 2–3, 5–6, 8·0, 10·6–11·3, 13, 18–19 years) and its close similarity with cycles in natural environmental phenomena as meteorological factors and heliogeophysical activity (HGA) suggested. This report aimed at verifying previous results on cyclic patterns of flu incidence by exploring whether flu annual cyclicity (seasonality) and trans-year (13 to <24 months) and/or multiannual (long-term, ⩾24 months) cycles might be present. For this purpose, a relatively long monthly flu incidence dataset consisting of absolute numbers of new cases from the Grand Baku area, Azerbaijan, for the years 1976–2000 (300 months) was analysed. The exploration of underlying chronomes or, time structures, was done by linear and nonlinear parametric regression models, autocorrelation, spectral analysis and periodogram regression analysis. We analysed temporal dynamics and described multicomponent cyclicity, determining its statistical significance. The analysis, considering the flu data specifically stratified in three distinct intervals (1976–1990, 1991–1995, 1996–2000), and also combinations thereof, indicated that the main cyclic pattern was a seasonal one, with a period of T = 12 months. Further, a number of multiannual cycles with periods T in the ranges of 26–36, 62–85 or 113–162 months were observed, i.e. average periods of 2·5, 6·1 and 11·5 years, respectively. Indeed, most of these cycles correspond to similar cyclic parameters of HGA and further analyses are warranted to investigate such relationships. In conclusion, our study revealed the presence of multicomponent cyclic dynamics in influenza incidence by using relatively long time-series of monthly data. The specific cyclic patterns of flu incidence in Azerbaijan allows further, more specific modelling and correlations with environmental factors of similar cyclicity, e.g. HGA, to be explored. These results might contribute more widely to a better understanding of influenza dynamics and its aetiology as well as to the derivation of more precise forecasted estimates for planning and prevention purposes.