We will see in this talk how doubly parabolic Baker domains can appear as a limit of attracting basins in parameter families of entire functions. More specifically, we show that, if an attracting fixed point escapes to infinity while its multiplier tends to one, the limiting function has a doubly parabolic Baker domain. Conversely, we show that any function with a doubly parabolic Baker domain can be approximated locally uniformly by functions with an attracting periodic orbit whose multiplier tends to one.