2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228593Nonstandard 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" $\vecω$ needs to be constructed. Once this is done, the first limit-ordinal rank $ω$ can be attained. This procedure can be continued on to still higher ranks.10 pagesCombinatorics05C99text