Background and objectiveAnalysis of rhythmic data has become an important aspect in biological and medical as well as in other fields of science. Several nonparametric methods aimed at such analyses have been reported in recent years. However, parametric methods based on trigono-metric regression still reflect several advantages. Different software packages for parametric analysis of rhythmic data have been made available recently. These are mostly based on a single-component cosinor model, which is not able to describe asymmetric oscillations that might reflect multiple peaks per period. Moreover, a basic cosinor model is unable to describe oscillations that are changed (namely forced or damped) with time. Here, we present some important extensions of the recently developed CosinorPy Python package to address these gaps.MethodsThe extended version of CosinorPy provides functionalities to perform a detailed individual or comparative analysis of rhythmic behaviour reflecting (1) multiple asymmetric peaks per period, (2) forced, damped or sustained oscillations, and (3) accumulation or reduction of MESOR with time. In all these cases the package is able to assess the (differential) rhyth-micity parameters, evaluate their significance and confidence intervals, and provide a set of publication-ready figures.ResultsWe demonstrate the package on some typical scenarios incorporating different types of oscillatory dynamics, such as asymmetric, damped, and forced oscillations. We show that the proposed implementation of a generalised cosinor model is able to reduce the error of estimated rhythmicity parameters in cases that tend to be problematic for alternative models. The implementation of the presented package is available together with the scripts to reproduce the reported results at https://github.com/mmoskon/CosinorPy.ConclusionAccording to our knowledge, CosinorPy currently presents the only implementation that is able to cover the above scenarios using a parametric model with vast applications in biology and medicine as well as in other scientific domains.