I succesfully passed the TOEFL test, in order to be accepted for an undergraduate degree two years ago.I have to do the same for a master degree?My question stems from the fact that the validity of this test is just for 2 years.

If you passed your undergraduate degree and it was taught and examined in English (from a recognised university in the UK, Australia, New Zealand, Canada or the USA) then you will not need to take another English language test.