In Quenya where m appeared after another nasal it generally became w, so that nm > nw and ñm > ñw > ñgw. This is true mainly of combinations that arose when voiced stops became nasals before nasals and [up through the mid 1950s] the prior change whereby voiceless stops were voiced before nasals. Tolkien described these sound changes in the Outline of Phonetic Development (OP1) from the 1940s, which indicates the shift occurred in Parmaquesta [PQ]:

Since ñ did not occur as a suffixal consonant, and m was seldom used after labials (p, ph, b) we are concerned only with pn > bn > mn; tn > dn > nn; tm > dm > nm; kn > gn > ñn; km > gm > ñm. All these combinations are said still to appear in AQ, but in classical PQ: nm > nw (a favoured group); and ñm > ñw > ñgw. Thus √TEK “write”: *tekma “writing, grammar” > tegmā, teñma, teñgwa (OP1: PE19/43).

In Tolkien’s later writing, voiceless stops were no longer voiced before nasals and instead [n], [m] became [t], [w] after voiceless stops. Thus, the development of new nasal + m combinations arose only from voiced stops + m. Tolkien’s description of the nm changes in the Outline of Phonology (OP2) in the 1950s are somewhat different from those of the 1930s:

nm became either mm (with forward assimilation of articulation point common [?with] nasals), or nw (a favoured group) by dissimilation. Which is the strictly “phonetic” development is not certain, since “etymological” considerations were at any period likely to have effect. mm was probably the older and more phonetic result — since it occurs in cases where the original stem was obscured and etymology of the word as a whole was forgotten; nw occurs usually when the stem ended in n + m-suffix, or in d (there are no known cases of dm > nm > mm): sc. when it was felt desirable to retain the dental quality of the first element of the group. mm also occurs in compounds where it was desirable to preserve the 2nd element or initial of the 2nd word, as Elemmíre (name) = “Elven-gem” or “Star-gem” (OP2: PE19/96).

Despite the comments above, primitive nm became nw in all attested phonetic developments from this conceptual period, and the assimilation nm > mm appears only in compounds. Compare:

• ✶ndanmē > Q. nanwe “ebb, lowtide” (VT48/26).
• ✶khadmā [> *χanmā] > Q. hanwa “seat” (PE22/148).
• ✶phanmā > Q. fanwa “veil” (PE17/180).
• Q. Elemmacil “*Star-sword” = elen + macil (UT/45).
• Q. Elemmírë “*Star-gem” = elen + mírë (S/48, PE19/96).

Elsewhere in OP2 Tolkien said: “in compounds ... these the initial m/mb, n/nd of the second element usually became m, n; and similarly ñ, ñg > ñ” (OP2: PE19/81). This helps explain why compounds were immune to nm, ñm > nw, ñgw, since the initial nasal sounds in the second element generally had the same phonetic developments as if it were in word-initial position.

As for the combination ñm, in the first drafts of OP2 from the early 1950s, ñm > ñw > ñgw just as it did in OP1:

In these cases the historical results were the same as for stops + mn. mn, mm, nn remained unchanged. nm > nw. ñm > ñw > ññw > ñgw.

This is consistent with the derivation ✶wagme [> wañwe] > Q. vangwe “blow” from 1957, and in notes from 1969 Tolkien said:

-nm > nw̃ > nw ... ŋm = ñw > ngw (PE22/149).

However, in green-ink revisions to OP2 from around 1970, Tolkien introduce a new phonetic development, with ñ vanishing with compensatory lengthening:

Owing to the disappearance of medial ñ [in Common Eldarin] the historical developments retaining a stem-nasal were specially liable to later alteration. Thus tēma “series” fr[om] TEG- “line”: tegma, “direct[ion], process” > teñma > tę̄ma (OP2: PE19/97).

This vanishing of ñ (< g) before m with vowel-lengthening was a very late idea, and the example Tolkien gave was Q. téma < teg-mā. In earlier writings this word was derived from ✶teñ-mā (PE19/82) or ✶teʒ-mā (PE18/104) where the consonant loss with compensatory lengthening (> tēmā) was ancient, maybe even in CE.

Conceptual Development: In the Qenya Phonology from the 1910s Tolkien said that basically all combinations of nasals + w became ñgw: “ñ, n, m, ŋ + ẇ [>] ngw” (PE12/23), though the dot in ẇ may indicate this sound change may have in some cases been limited to w derived from ɣ͡w [ɣʷ]. The developments of nm in the Early Qenya period is hard to determine given the lack of examples.

Neo-Quenya: As suggested in the entry on how [n], [m] became [t], [w] after voiceless stops and aspirates, for purposes of Neo-Quenya it might be better to ignore the paradigm described in 1970 revisions to OP2 and retain the developments whereby (a) voiceless stops were voiced before nasals and (b) ñm > ñgw, the latter of which seems to be Tolkien’s normal development prior to 1970.