Hello,

I'm now working as a fellow postdoc in USA and I'm a resident of United Kingdom,
I was informed that I do not have to pay taxes in USA if I'm going to stay for less than 2 years. Does it mean that if I stay for longer than two years, I will have to pay the tax back, or that I will have to start paying the tax after two years (without paying the tax for the first two years).

Thank you

This is from IRS publication 901. Tax Treaties
"A professor or teacher who is a resident of the United Kingdom on the date of arrival in the United States and who is in the United States for not longer than 2 years primarily to teach or engage in research at a university, college, or other recognized educational institution is exempt from U.S. income tax on income for the teaching or research. If the individual's 2-year period is exceeded, the exemption is lost for the entire visit, including the 2-year period.
The exemption does not apply to income from research carried on mainly for the private benefit of any person rather than in the public interest."

You must have J1 visa for Research. Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents

Thank you very much, that's the information I was looking for.