如果国外领导始终不回复审批邮件，您可以尝试以下方法用英文催促他们：

1. Polite Reminder: Dear [领导的姓名], I hope this email finds you well. I wanted to kindly remind you about the pending approval for [具体事项]. Your prompt response would be greatly appreciated. Thank you for your attention to this matter.
2. Follow-up Email: Dear [领导的姓名], I hope you are doing well. I wanted to follow up on my previous email regarding the approval for [具体事项]. I understand you may be busy, but I would greatly appreciate your prompt response as it is crucial for [相关事项]. Thank you for your attention and assistance.
3. Escalation: Dear [领导的姓名], I hope this email finds you well. I have been waiting for your response regarding the approval for [具体事项] for quite some time now. As this matter is time-sensitive and important for the progress of [相关事项], I kindly request your immediate attention and response. Thank you for your understanding and cooperation.
4. Seek Assistance: Dear [领导的姓名], I hope you are doing well. I understand you may be busy, but I have been waiting for your response regarding the approval for [具体事项] for an extended period. In order to move forward with the project, I kindly request your assistance in expediting the approval process. If there are any concerns or additional information required, please let me know. Thank you for your support.

请注意，以上提供的回复仅供参考，具体内容可以根据实际情况进行调整。同时，尽量使用礼貌和尊重的语气，以增加对方回复的可能性。