Subject: is there any chance that at any stage immortality can develop?

ok first try to understand my example. suppose there are two moths of 
different species. one can coumouflage and other can't. so the more adapted 
will survive and live longer than the other. i mean to say that all the 
adaptations are focused on the better surviving skills of the animal and thus 
on his longetivity of life. and the process of reproduction is also based on 
the survival of the species. so in near future is it possible to that a 
species develops which is able to avoid its natural death at least for a few 
thousand or million years and has a very slow reproductive rate (to avoid over 
crowding)  

Re: is there any chance that at any stage immortality can develop?