No, they are not homonyms.

They are not homonyms

Sorry, I do not understand the answers: how two identical species-level names (fossilis) in the same genus (Cervus) can be "not homonyms"??? Unless one (or both) of them are nomenclatorily "unavailable" (i.e. formally non-existent), they are evident homonyms!

Dear Roman Bohdan Holynski,

There are two different species of the genus Cervus, which are here under consideration: Cervus elaphus and Cervus canadensis. Their spellings are altogether different from each other. Hence, the question of their being synonyms does not arise. "fossilis" is therefore of no importance in determining homonymy.

R K Saxena

I thank everybody who shared their opinion on this question. I have reported C. elaphus fossilis and C. canadensis fossilis as homonyms in my recent paper: Article A new form of wapiti Cervus canadensis Erxleben, 1777 (Cervi...

The important argument for this conclusion is that subspecies names theoretically may be elevated to species rank, and thus those names become obvious primary homonyms as Prof. Hołyński suggested here.

ICZN: Art. 53.3: "Two or more available species-group names having the same spelling are homonyms if they were originally established in combination with the same generic name (primary homonymy), or when they are subsequently published in combination with the same generic name (secondary homonymy)" (bold-face mine: RBH) - decisive is combination with generic name, not "ranks" of the respective identical species-level names! Here the generic name in both cases is the same: Cervus.

Yes, the generic name in both cases is the same: Cervus. But the species epithet are different, e.g. "elaphus" and "canadensis". Thus the resulting combinations Cervus elaphus and Cervus canadensis are different.

I think I might be missing something. I'm troubled by the "fossilis" subspecies name. in vertebrate paleontology we don't distinguish between extinct, extant, and fossil, typically treating them all the same with genus and species names. Does it merely denote an extinct or fossil variety? If so, it should be dropped. If not (they are both extant), one of them changed such that the subspecies names are unique. Following this step, there would be no issues with homonymy or synonymy.

From what had Roman Croitor written (I am neither palaeontologist nor theriologist so I have no own opinion) it seems that in both instances "fossilis" is a formal name of a taxon (subspecies), both in the same genus (Cervus), so Cervus canadensis fossilis Znansky 1925 is evidently a junior homonym of Cervus elaphus fossilis Goldfuss 1821, irrespective of whether they are extinct or extant! The question may be only whether they are primary homonyms (both have been originally - by Goldfuss 1821 and Znansky 1925 - described as Cervus (in which case Znansky's name is invalid forever), or secondary (described - one or both of them - with different generic names and only by later taxonomists transferred to Cervus) in which situation the name might be "resurrected" by those who consider them representatives of different genera.