  We describe weak BCC-algebras (also called BZ-algebras) in which the
condition $(xy)z=(xz)y$ is satisfied only in the case when elements $x,y$
belong to the same branch. We also characterize branchwise commutative and
branchwise implicative weak BCC-algebras satisfying this condition. We also
describe connections between various types of implicative weak BCC-algebras.
