  Dynamical typicality refers to the property that two pure states, which
initially exhibit (almost) the same expectation value for some given observable
$A$, are very likely to exhibit also very similar expectation values when
evolving in time according to the pertinent Schr\"odinger equation. We unify
and generalize a variety of previous findings of this type for sufficiently
high dimensional quantum mechanical model systems. Particular emphasize is put
on the necessary and sufficient conditions, which the initial expectation value
and the spectrum of $A$ have to fulfill.
