About your sentence : "there are no animal species that do not age".

Well, I hate to use Wikipedia for that, but current observations seem to disagree with this:

http://en.wikipedia.org/wiki/List_of_long-living_organisms

You'll see in that post that there are several species for which we find that mortality does not increase with age, i.e. they do not appear to age.

Now, I am not a specialist on the subject, so I will not be able to go into debate whether this is truth or fiction, but I have heard/seen this mentioned in several sources.