  Dilatively stable processes generalize the class of infinitely divisible
self-similar processes. We reformulate and extend the definition of dilative
stability introduced by Igl\'oi (2008) using characteristic functions. We also
generalize the concept of aggregate similarity introduced by Kaj (2005). It
turns out that these two notions are essentially the same for infinitely
divisible processes. Examples of dilatively stable generalized fractional
L\'evy processes are given and we point out that certain limit processes in
aggregation models are dilatively stable.
