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Usually you have the right to appeal against a first decision on your asylum application. The procedure varies from country to country. So if you tell us in which country you were having your asylum procedure, we can help you to find out more about the next steps. You probably already received information about that along with the documents that denied your asylum application. Maybe you can get in touch with a counselling center to ask them about your options.
In general, an appeal against the first decision can be successful if you can provide fresh evidence that hasn't been taken into account during your initial procedure. It has to be something that shows that your situation changed for the worse (e.g. because the situation in your home country escalated recently).