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If you are already in the US, are not a US citizen you may wish to apply for asylum for two reasons. First, if returning to your home country could pose a serious threat to you based on your race, political views, or religion you can apply for refugee or asylum status. Second, if you are facing removal from the US you can apply for asylum in order to halt this proceeding in some cases. To apply for asylum in the US, you will need to file USCIS form I-589 (Application for Asylum and Withholding of Removal), which will detail why you are applying for this status.