If the marriage is bona fide and in good faith, yes. If it is to obtain an immigration benefit, no. Speak with and retain an attorney if it is a bona fide marriage. My firm handles such cases.
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As my colleague stated, if USCIS determines that the marriage is bona fide, then they would approve the petition that the US Citizen files for you. But you should be aware that USCIS will likely take a close look at your relationship, due to the age difference. If there are parents involved who might raise complaints to USCIS, that could complicate things as well.
I suggest that you consult with an immigration attorney about this situation, to get an honest assessment of the likelihood of success in this case.
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If the marriage and relationship are legitimate (meaning based on love) you can lawfully marry and petition for a green card. However, the age difference will definitely be an issue, as will the length of the relationship (it cannot be more than 3 years old or you'd be admitting to a crime) and other possible issues. Consult with an immigration lawyer before making an decisions.
As long as the marriage is legitimate you can get married and file the adjustment of status application. However, because of the difference in age you should be ready to show substantial evidence that the marriage is legitimate. Since your fiance is already over 18 the fact that her parents dont agree is not relevant.
I agree with my colleagues, but be aware of the affidavit of support requirements.
Pay special attention to the provisions regarding the income requirements on page 2.