Data on the dynamics of malaria incidence, admissions and mortality and their best possible description are very important to better forecast and assess the implementation of programmes to register, monitor (e.g. by remote sensing) and control the disease, especially in endemic zones. Semi-annual and seasonal cycles in malaria rates have been observed in various countries and close similarity with cycles in the natural environment (temperature, heliogeophysical activity, etc.), host immunity and/or virulence of the parasite suggested. This study aimed at confirming previous results on malaria cyclicity by exploring whether trans-year and/or multiannual cycles might exist. The exploration of underlying chronomes (time structures) was done with raw data (without smoothing) by linear and nonlinear parametric regression models, autocorrelation, spectral (Fourier) and periodogram regression analysis. The strongest cyclical patterns of detrended malaria admissions were (i) annual period of 1·0 year (12 months or seasonality); (ii) quasi-biennial cycle of about 2·25 years; and (iii) infrannual, circadecennial cycle of about 10·3 years. The seasonal maximum occurred in May with the minimum in September. Notably, these cycles corresponded to similar cyclic components of heliogeophysical activity such as sunspot seasonality and solar activity cyclicities and well-known climate/weather oscillations. Further analyses are thus warranted to investigate such similarities. In conclusion, multicomponent cyclical dynamics of cerebral malaria admissions in Papua New Guinea were observed thus allowing more specific analyses and modelling as well as correlations with environmental factors of similar cyclicity to be explored. Such further results might also contribute to and provide more precise estimates for the forecasting and prevention, as well as the better understanding, of the dynamics and aetiology of this vector-borne disease.