Hello,

I am a hungarian research fellow in Oklahoma City, at the Oklahoma University. I have arrived to the US on 08. 17. 2011 as a J1 exchange visitor. Based on my DS2019 form, I started my work at 08-22-2011, and I have to finish it at 08-21-2013. It is a 2 years period exactly. I was REQUIRED to enter the US BEFORE the start date, otherwise my J1 visa status would have been jeopardized. Now, I got my first salary (for september), and taxes were taken away from it, because they counted the period from 08. 17. 2011. To 08-21-2013, which is 5 days more than 2 years. So, my question is the following: Do I nedd to pay any taxes? Can I get back this money (e.g.in the next year?) I can not understand exactly this treaty between the USA and Hungary, and I do not know why my situation is not an exemption in the taxation, because my J1 visa is valid for 2 years exactly.
Thank you your answer in advance!

I could claim for my money or not?

There is no retroactive clause in the tax treaty with Hungary. Therefore, you are exempt for 2 years from being taxed (unless your salary comes from a private institution like HHMI for example).
If your university is withholding taxes, you can claim them back with your tax return you file next year in April. Since you are a non-resident alien, you would not be liable for social security and medicare, so make sure they don't withhold those.
The relevant article from the US -Hungary tax treaty would be:

ARTICLE 17
Teachers
1. Where a resident of one of the Contracting States is invited by the Government of the other
Contracting State, a political subdivision or a local authority thereof, or by a university or other
Recognized educational institution in that other Contracting State to come to that other Contracting State
For a period not expected to exceed 2 years for the purpose of teaching or engaging in research, or
Both, at a university or other recognized educational institution, and such resident comes to that other
Contracting State primarily for such purpose, his income from personal services for teaching or research
At such university or educational institution shall be exempt from tax by that other Contracting State for a
Period not exceeding 2 years from the date of his arrival in that other Contracting State.
2. This Article shall not apply to income from research if such research is undertaken not in the
Public interest but primarily for the private benefit of a specific person or persons.

The US -Hungary tax treaty writes: the person shall be exempt from tax by that other Contracting State for a
Period not exceeding 2 years from the date of his arrival in that other Contracting State.
And you said:I am an exempt for 2 years from being taxed
So, Can I be an exempt from aug 17 2011 (arraival date) to aug 16 2013
OR: Can I be an exempt from aug 22 2011 (I am being taxed) to aug 21 2013?

The 2 year period counts from the day you arrive.