I was a J-1 research scholar entered in US May 3rd 2004 and left US (for good) August 21st 2006. Now I'm back to Italy.
This is what I understood about my situation.
I was a non-resident alien from May 3rd 2004 until December 31st 2005 (because in my third year I stayed more 183 days).
I became a resident alien during 2006, therefore I am considered resident alien starting January 1st 2006.
Then I left US during 2006, therefore at the end of the year I'm a non-resident.

Then about filing, this is what I understood.
I have to file 1040NR because at the end of the tax year I'm a non-resident.
I should fill my 1040NR with the income of the whole year, both the part I was a resident and the part I was a non-resident.
I should attach a statement explaining my income during the period I was a resident (Jan 2006-Aug 2006).
In 1040NR my income for the period I was a non-resident (Sept 2006- Dec 2006) should be zero because I had
- wages as teacher from Italy and they are not connected to US
- interests from a US bank account and they are not taxed for non-resident

Is the way I'm going to file correct?
I have two more questions (but I'm going to divide them in different e-mails)
Thanks!

Elena:

What you need to file is an expatriate DUAL-STATUS return.

It will consist of BOTH Form 1040NR (as the dual-status return) and Form 1040 (as the dual-status statement).

All tax computations are done on the Form 1040NR, but you U.S.-sourced income during your resident period is shown on the Form 1040.

This is NOT a return for the lay person. You should get a tax professional with experience in this type of return to help you.