  Self-similarity of systems is very popular and intensively developing field
during last decades. To this field belong so-called stable distributions and
their generalization. In Klebanov and Sl\'amov\'a (2014) there was given an
approach to define additive systems with the property of random self-similarity
- casual stability (c.s.). Here we continue study the notion of casual
stability for additive systems of random variables (r.v.). We also give a
modification of this definition and spread them on multiplicative systems of
r.v. and on the system with operations of taking minimum or maximum of r.v. The
case of systems with a random number of elements is also considered.
