The current study explores noun-noun collocations in English. The main problem which the study attempts to tackle is the difficulty encountered by undergraduate, English department students in predicting noun-noun collocations in English. The hypothesis on which the study is based is the existence of hundreds of noun-noun collocations in English, be they noun and/or noun (binomial phrases), e.g. fish and chips, friend or foe; or noun + of-phrase combinations, e.g. sheet of paper, cup of tea. As regards the study approach adopted, the paper advocates Biber et al. (1999) (see sections 6 and 7). This approach is within 'lexical collocations', which is in contrast to 'grammatical collocations' in which a preposition is used with a noun, a verb or an adjective, e.g. by accident, account for, amazed at. The aim of the study is to define and explain different types and combinations of binomial phrases and noun + of-phrases. The results of the two tests administered to measure fourth year, English department students' mastery of different categories of lexical collocations (100 participants who sat a 40-item twofold tests) show that students face great obstacles in mastering collocations. Noun + noun sequences like water supplies, chess board, exam papers, speech impediment, and press release, are out of the scope of this study. .