The Test of English as a Foreign Language (or TOEFL) is a stem-winder. It's a literacy test and I have a Russian friend who took it about three times before she passed it. She worked really hard and said the test itself was awful.
I went over the practice test with her and I could see where someone who didn't have an excellent grasp of English would have problems. In fact, native English speakers who didn't have a degree in the subject (like I do) might not have done very well. It's a really tough test and I wouldn't have wanted to take it if I were not a native English speaker.