[Fingolfin of the Noldor]

it's true, they are fallen elves...

Actually, as I have said before, it is not exactly that simple. All that is put forth in the Silmarillion is a hypothesis of the Noldor nothing more:

But of those unhappy ones who were ensnared by Melkor little is known of a certainty. For who of the living has descended into the pits of Utumno, or has explored the darkness of the counsels of Melkor? Yet this is held true by the wise of Eressea, that all those of the Quendi who came into the hands of Melkor, ere Utumno was broken, were put there in prison... "Of the Coming of the Elves" The Silmarillion

That said though Tolkien's actual view of the matter went throw quite a bit of change(see the Myths Transformed section of Morgoth's Ring) his final view dows seem to be as CT points out that Orcs must ahve been ultimately derived from men. Here is an excerpt from his final essay on the matter:

The origin of Orcs is a matter of debate...
Those who believe that the Orcs were bred from some kind of Men, captured and perverted by Melkor, assert that it was impossible for the Quendi to have known of Orcs before the Separation and the departure of the Eldar. For though the time of the awakening of Men is not known, even the calculations of the loremasters that place it earliest do not assign it a date long before the Great March began, certainly not long enough before it to allow for the corruption of Men into Orcs. On the other hand, it is plain that soon after his return Morgoth has at his command a great number of these creatures, with whom he ere long began to attack the Elves. There was still less time between his return and these first assalts for the breeding of Orcs and for the transfir of their host westward.
This view of the origin of orcs thus meets with difficulties of chronology. But though Men may take comfort in this the theory remains nonetheless the most probable. It accords with all that is known of Melkor, and of the nature and behavior of Orcs and Men... 'Orcs' pg 416-17 Morgoth's Ring

But keep in mind:

Elves and Men are evidently in biological terms one race, or they could not breed and produce fertile offspring - even as a rare event... ~unsent letter #153 The Letters of JRR Tolkien

[ July 27, 2002: Message edited by: Fingolfin of the Noldor ]