In this paper we deal with the \abDis\ of an $MV$-algebra $\Cal A$,
where $\alpha$ and $\beta$ are nonzero cardinals. It is proved that
if $\Cal A$ is singular and \a2dis, then it is \aadis. We show that
if $\Cal A$ is complete then it can be represented as a direct
product of $MV$-algebras which are homogeneous with respect to
higher degrees of distributivity.
