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No. In fact, private student loans are not eligible for consolidation through the Federal Direct Loan Consolidation Program at all. They can however, be refinanced separately. Two ways to do this are through a home equity loan (for homeowners only) or through education lenders. Before signing on the dotted line, be sure to evaluate any fees, whether or not the interest rate is fixed, and whether the lender charges prepayment penalties. Go to FinAid for a list of education lenders – but remember that for federal loans you will likely get the best rates and benefits by going through the Federal Direct Loan Consolidation Program.
In the past, students could obtain Federal Family Education Loans (FFEL), which were actually provided by private lenders and guaranteed by the federal government. These loans are no longer provided, although existing FFEL loans can still be consolidated under the Federal Direct Loan Program. This is the only case in which a “private” loan can be consolidated with a federal loan (since they are in fact guaranteed by the federal government).