Hi and welcome to Just Answer!
You would determine their residency status for tax purposes (please do not confuse with residency requirements for immigration purposes)
See IRS publication 519 - chart on page 5 - www.irs.gov/pub/irs-pdf/p519.pdf
Please be aware that residency status is determined separaetly for each tax year.
According to Substantial Presence Test - the person will be considered a US resident for tax purposes if he/she meets the substantial presence test for calendar year 2011. To meet this test, the alien must be physically present in the United States on at least:
1. 31 days during 2011, and
2. 183 days during the 3-year period that includes 2011, 2010, and 2009, counting:
-- All the days you were present in 2011, and
-- 1/3 of the days you were present in 2010, and
-- 1/6 of the days you were present in 2009.
Considering your information - your parents are resident aliens for tax purposes - and you might be able to claim them as dependents
To claim parents as dependents - they do not have to live with you but there are some other requirements.
Let me know if you need any help.