Hi, I am an Israeli scholar (postdoc) on J-1 visa. I came to the US in December 2006, but started working (and receiving salary) from Jan 1, 2007. For the first 2 years (2007-2008) I have claimed tax benefits under US-Israel tax treaty. Since I wasn't paying federal income tax for the first two years I didn't file tax return, which I now understand was not a right thing to do. Anyway, during 2009 I paid all the taxes and now I am going to file a tax return for the first time. My questions are:

1) Since I haven't paid income tax in the US for 2007-2008, I should pay them in Israel, right?
2) Is there any fine for not submitting the tax return forms for 2007-2008? Can I submit them retro-actively?

1. About Israel taxes, no idea. This forum is mainly for the U.S. taxes.
You should file tax return and Form 8843 for 2007 and 2008. You can still file it. On tax return, report your total income and then claim tax treaty deduction so that net income is nil

Did you get a salary (W2) or a scholarship in 2007-2008? The salary would not fall under the treaty. A scholarship is tax free in Israel, so you don't have to pay taxes for it in Israel.