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Why would they have a choice? Both their parents are elves.
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No, Elladan and Elohir were the sons of an Elf (Celebrian) and a Half-Elf (Elrond) and so had mortal blood. By default, they would normally share the fate of Men. But, like their father, they were given the choice between mortality and immortality. Although they were to exercise that choice by the time their father left for Valinor, they appear to have been given a time extension and we never learn of which choice they made.
As for the descendants of Elros, they were bound by Elros' choice. They were therefore mortal (as were the descendants of Aragorn and Arwen).
I found
this and other threads (like the search function [img]smilies/wink.gif[/img] ) to be very helpful in answering all my questions on this issue.