This paper suggests an evolving possibilistic approach for fuzzy modelling of time-varying processes. The approach is based on an extension of the well-known possibilistic fuzzy c-means (FCM) clustering and functional fuzzy rule-based modelling. Evolving possibilistic fuzzy modelling (ePFM) employs memberships and typicalities to recursively cluster data, and uses participatory learning to adapt the model structure as a stream data is input. The idea of possibilistic clustering plays a key role when the data are noisy and with outliers due to the relaxation of the restriction on membership degrees to add up unity in FCM clustering algorithm. To show the usefulness of ePFM, the approach is addressed for system identification using Box & Jenkins gas furnace data as well as time series forecasting considering the chaotic Mackey-Glass series and data produced by a synthetic time-varying process with parameter drift. The results show that ePFM is a potential candidate for nonlinear time-varying systems modelling, with comparable or better performance than alternative approaches, mainly when noise and outliers affect the data available.