The parallel-functional language Eden has a non-deterministic construct, the process abstraction merge, which interleaves a set of input lists to produce a single non-deterministic list. Its non-deterministic behaviour is a consequence of its reactivity: it immediately copies to the output list any value appearing at any of the input lists. This feature is essential in reactive systems and very useful in some deterministic parallel algorithms. The presence of non-determinism creates some problems such that some internal transformations in the compiler must be disallowed. The paper describes several non-determinism analyses developed for Eden aimed at detecting the parts of the program that, even in the presence of a process merge, still exhibit a deterministic behaviour. A polynomial cost algorithm which annotates Eden expressions is described in detail. A denotational semantics is described for Eden and the correctness of all the analyses is proved with respect to this semantics.