Abstract: Existing research has shown that a multilingual pre-trained language model fine-tuned with one (source) language also performs well on downstream tasks for non-source languages, even though no fine-tuning is done on these languages. However, there is a clear gap between the performance of the source language and that of the non-source languages. This paper analyzes the fine-tuning process, discovers when the performance gap changes and identifies which network weights affect the overall performance most. Additionally, the paper seeks to answer to what extent the gap can be reduced by reducing forgetting. Based on the analysis results, a method named Fine-tuning slow and fast with four training policies is proposed to address these issues. Experimental results show the proposed method outperforms baselines by a clear margin.