A braided Ann-category $\A$ is an Ann-category $\A$ together with the
braiding $c$ such that $(\A, \otimes, a, c, (I,l,r))$ is a braided tensor
category, and $c$ is compatible with the distributivity constraints. The paper
shows the dependence of the left (or right) distributivity constraint on other
axioms. Hence, the paper shows the relation to the concepts of {\it
distributivity category} due to M. L. Laplaza and {\it ring-like category} due
to A. Frohlich and C.T.C Wall.

The center construction of an almost strict Ann-category is an example of an
unsymmetric braided Ann-category.