The main challenge of continual learning is \textit{catastrophic forgetting}. Because of processing data in one pass, online continual learning (OCL) is one of the most difficult continual learning scenarios. To address catastrophic forgetting in OCL, some existing studies use a rehearsal buffer to store samples and replay them in the later learning process, other studies do not store samples but assume a sequence of learning tasks so that the task identities can be explored. However, storing samples may raise data security or privacy concerns and it is not always possible to identify the boundaries between learning tasks in one pass of data processing. It motivates us to investigate rehearsal-free and task-free OCL (F2OCL). By integrating prompt learning with an NCM classifier, this study has effectively tackled catastrophic forgetting without storing samples and without usage of task boundaries or identities. The extensive experimental results on two benchmarks have demonstrated the effectiveness of the proposed method.