Hello, I came to US in December 2008 with J2 visa, from 2009 till now, I am working as a research fellow in Boston. I know my husband(J1) has no any tax responsibility during 2009. Am I also have no any tax? If I have to pay tax, am I a resident alien or a non-resident alien? Do I need pay all the tax?

On J1 or J2 you are nonresident for 2 years.