Abstract: 
It is proved for Abelian groups that the Reidemeister
coincidence number of two endomorphisms $\phi$ and $\psi$
is equal to the number of coincidence points of $\widehat\phi$
and $\widehat\psi$ on the unitary dual, if the Reidemeister number is finite.
An affirmative
answer to the bitwisted Dehn conjugacy problem
for almost polycyclic groups is obtained.
Finally, we explain why the Reidemeister numbers are always infinite
for injective endomorphisms of Baumslag-Solitar groups.

1. Instytut Matematyki
   Uniwersytet Szczeciński
   ul. Wielkopolska 15
   70-451 Szczecin, Poland
   and
   Boise State University
   1910 University Drive
   Boise, ID 83725-155, USA