  We extend F.Pastjin's construction of uniform decomposable chains of finite
rank to those of rank 'finite over a limit' and investigate infinite products
and unions of such chains. We derive an extension of Pastjin's characterisation
to uniform decomposable chains of small transfinite rank (less than or equal to
'omega+omega'). We conclude by indicating how the resulting descriptions can be
iterated to chains of rank 'omega to the omega', and beyond.
