Title: Does Continual Learning Equally Forget All Parameters?. Abstract: Distribution shift (e.g., task or domain shift) in continual learning (CL) usually results in catastrophic forgetting of neural networks. Although it can be alleviated by repeatedly replaying buffered data, the every-step replay is time-consuming and the memory to store historical data is usually too small for retraining all parameters. In this paper, we study which modules in neural networks are more prone to forgetting by investigating their training dynamics during CL. Our proposed metrics show that only a few modules are more task-specific and sensitively alters between tasks, while others can be shared across tasks as common knowledge. Hence, we attribute forgetting mainly to the former and find that finetuning them only on a small buffer at the end of any CL method can bring non-trivial improvement. Due to the small number of finetuned parameters, such ``Forgetting Prioritized Finetuning (FPF)'' is efficient on both the computation and buffer size required. We further propose a more efficient and simpler method that entirely removes the every-step replay and replaces them by only $k$-times of FPF periodically triggered during CL. Surprisingly, this ``$k$-FPF'' performs comparably to FPF and outperforms the SOTA CL methods but significantly reduces their computational overhead and cost. In experiments on several benchmarks of class- and domain-incremental CL, FPF consistently improves existing CL methods by a large margin and $k$-FPF further excels on the efficiency without degrading the accuracy. We also empirically studied the impact of buffer size, epochs per task, and finetuning modules to the cost and accuracy of our methods.