  The process of dynamical decoherence may cause apparent superselection rules,
which are sometimes called `environmentally induced' or `soft'. A natural
question is whether such dynamical processes are eventually also responsible
for at least some of the superselection rules which are usually presented as
fundamentally rooted in the kinematical structure of the theory (so called
`hard' superselection rules). With this question in mind, I re-investigate two
well known examples where superselection rules are usually argued to rigorously
exist within the given mathematical framework. These are (1) the Bargmann
superselection rule for the total mass in Galilei invariant quantum mechanics
and (2) the charge superselection rule in quantum electrodynamics. I argue
that, for various reasons, the kinematical arguments usually given are not
physically convincing unless they are based on an underlying dynamical process.
