yes your parents can buy the home

they can pay cash

If they wish to obtain a mortgage, and they are also paying on an existing home...

they will need a credit score of at least 620
and about a 45% debt to income ratio
not to mention an income that can support their existing debts plus the new home

They can certainly buy it for you. Are they mortgaging it or paying cash? They can buy it for you and have you on the title either way. If this is your first home, you should qualify for the $8000 tax credit if you close before Nov. 30th. They won't have a tax ramification for purchasing. If they mortgage it, they can get a deduction for their taxes. Tax "ramifications" occur from capital gains when you sell. Your agent should be able to help you with all of it. If you don't have an agent helping you, or if you'd like more information, I'll be happy to help you free of charge. You can email me at tiphanie@elite-realty-group.com or call me at 225-278-5155. Good luck!