Twin, Triplet, Quadruplet, Quintuplet, Sextuplet, Heptuplet, Octuplet, Nontuplet, Decuplet, ...
Is this the end of the list of this kind of words? Can anyone continue the list further?
By the way, is "septuplet" the same as "nontuplet"? Thanks for reading and replying!
Roland
Twin, Triplet, Quadruplet, Quintuplet, Sextuplet, Heptuplet, Octuplet, Nontuplet, Decuplet, ...

"Heptuplet" should be "septuplet"; this series is derived from Latin, not Greek. And there's only one T in nonuplet.
Is this the end of the list of this kind of words? Can anyone continue the list further?

Based on related Latin and English series, it should continue to 20: undecuplet, duodecuplet, tredecuplet, quattuordecuplet, quindecuplet, sedecuplet, septendecuplet, octodecuplet or perhaps duodevigintuplet, novendecuplet or perhaps undevigintuplet, and vigintuplet.

In some cases other spellings may be possible. "Quindecuplet" is the only one of these words that I've heard of actually being required so far, and Google shows more hits for the spelling "quindecaplet".
By the way, is "septuplet" the same as "nontuplet"?

See above.

Mark Brader "MSB is an accepted explanation for men's Toronto misbehaviors. ... Just blame it on MSB (Email Removed) and everyone nods their heads." "TJ"

My text in this article is in the public domain.
Twin, Triplet, Quadruplet, Quintuplet, Sextuplet, Heptuplet, Octuplet, Nontuplet, Decuplet, ... Is this the end of the list of this kind of words? Can anyone continue the list further? By the way, is "septuplet" the same as "nontuplet"?septuplet = 7; nonuplet (note spelling) = 9.

You probably meant to ask about *"Heptuplet" (which should probably have been "heptad" or "hebdomad").
There are, of course, many choices instead of some of the words you have. Since these choices, including your words, can appear as nouns (with multiple meanings depending on context) and as adjectives (with multiple meanings depending on context), it is hard to know what sequence you really have in mind.
The real "*uplet" words are

2 couplet, cf. your "twin"
2 duplet, cf. your "twin"
4 quadruplet
5 quintuplet
6 sextuplet
7 septuplet, cf. your *"heptuplet"
8 octuplet
9 nonuplet, cf. your *"nontuplet"
10 decuplet
12 dodecuplet, add to your list

"triplet" of course is perfectly fine. It doesn't make my list because of the lack of a "u".