I agree with littlemanpoet. The Elves too fall. I think to Tolkien's mind, every story entailed some kind of fall. In the First Age, Fëanor's possessiveness precipitates the fall of the Noldor. They fall from peace and contentment (which is their nature) to belligerence and woe. The Elves fall again after the defeat of Melkor, for they now find that they are not perfectly content to have kingdoms in a corrupted, always decaying Middle-earth. They fall to the temptation to make the Rings of Power in an attempt to make Middle-earth more like Aman. But this is against the will of Eru.
Notice, however, that in both cases, the fall of the Elves is due to the influence of Melkor. It was Melkor who stole the Silmarilli, and it was Melkor who corrupted the fabric of Middle-earth and introduced decay. So Melkor is responsible not only for the fall of Men, but also for the fall of the Elves, just in different ways. And these falls both proceed from Melkor's own fall - his rebellion against Eru's supreme authority.
With the Elves he corrupts their ability to find peace and contentment in Arda. With Men, he corrupts their ability to find peace and contentment beyond Arda (which is their nature, as the "visitors").
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