  Nonstandard digraphs and transfinite digraphs have been defined and examined
in two prior technical reports. The present work examines digraphs that are
both nonstandard and transfinite. This requires a combination in certain ways
of the techniques used in the prior two works. We first construct herein
nonstandard transfinite digraphs for all the natural-number ranks. Then, a
special kind of nonstandard transfinite digraph having the "arrow rank"
$\vec{\omega}$ needs to be constructed. Once this is done, the first
limit-ordinal rank $\omega$ can be attained. This procedure can be continued on
to still higher ranks.
