  We consider quantum group theory on the Hilbert space level. We find all
unitary representations of three braided quantum groups related to the quantum
``ax+b'' group. First we introduce an auxiliary braided quantum group, which is
apparently not related to the quantum ``ax+b'' group, but easy to work with. We
find all unitary representations of this quantum group. Then we use this result
to find all unitary representations of another braided quantum group, whose
C*-algebra is generated by two (out of three) generators generating (in the
sense of Woronowicz) C*-algebra of the quantum ``ax+b''- group. We find all
unitary representations of this other braided quantum group. This is the most
difficult result needed to classify all unitary representations of the quantum
``ax+b'' group.
