Commonly known as immortal beings, the elves (Eldalië, Eldar) were the first born in Middle Earth, and the first of the races in the Children of Ilúvatar. While it is true that unlike the Men, for example, the elves (Eldar) do not grow old in body, but they still have a limit to their lives – which is the life of Arda. This means that the elves still do grow old, but they do so slowly.
They also have coherent body (hroä) and spirit (fëa), which also means that it is very similar to other races (but probably just in a slower pace). Since over the course of the years, they also deal with changes of desires, thoughts, impulses and moods, which lead to change in fëa (spirit). Their lives are dependent on the life of Arda.
The Eldar retained spirit, even after dwelling in Aman. They understood very well the differences between “breath” and the “spirit.”
Their ages can be counted in two different stages, growth years and life years – the former being = 3 löar (years), while the latter being longer, at 144 löar (years). So their ages depend on how they are calculated.