Dictionary definitions of nondualism, or any form of the word, are practically non-existent. You can find definitions of nondualism in encyclopedias, but not standard dictionaries.
Today I checked the Oxford English Dictionary Online, which includes quarterly updates, and there is no definition for nondual, nondualism, or nonduality.
Here is a definition I found today from
Webster’s Third New International Dictionary, Unabridged. Merriam-Webster, 2002.
Main Entry: non•dualism
Etymology: 1non- + dualism
1 : a doctrine of classic Brahmanism holding that the essential unity of all is real whereas duality and plurality are phenomenal illusion and that matter is materialized energy which in turn is the temporal manifestation of an incorporeal spiritual eternal essence constituting the innermost self of all things
2 : any of various monistic or pluralistic theories of the universe
Citation format for this entry:
“nondualism.” Webster’s Third New International Dictionary, Unabridged. Merriam-Webster, 2002. http://unabridged.merriam-webster.com (5 Jul. 2008).
I find the above to be a very limited definition of nondualism, although I like the metaphysical, almost poetic feel to it. I don’t know how useful the definition is.
Now here’s the definition of dualism from the Oxford English Dictionary Online. I’m showing it because it could serve as model for defining nondualism, except it would include quotations from different cultures and nondual perspectives.
Entry printed from Oxford English Dictionary Online
Copyright © Oxford University Press 2008
dualism SECOND EDITION 1989
( dju l z( )m) [f. DUAL + -ISM: cf. F. dualisme (1755 in Hatz.-Darm.).]
1. The condition or state of being dual or consisting of two parts; twofold division; duality.
1831 CARLYLE Sart. Res. II. ix, In Teufelsdröckh there is always the strangest Dualism. 1833 Diderot Misc. Ess. 1872 V. 53 Among the dualisms of man’s wholly dualistic nature, this we might fancy was an observable one. 1841-4 EMERSON Ess., Compensation Wks. (Bohn) I. 41 An inevitable dualism bisects nature, so that each thing is a half, and suggests another thing to make it whole. 1877 E. CAIRD Philos. Kant ii. 12 A dualism between knowing and being, between the ‘me’ and the ‘not me’.
2. Gram. The fact of expressing two in number.
1874 SAYCE Compar. Philol. vii. 276 We find many others [languages] in which the formal expression of plurality has never passed beyond that of dualism.
3. A theory or system of thought which recognizes two independent principles. spec.
a. Philos. The doctrine that mind and matter exist as distinct entities; opposed to idealism and materialism.
b. The doctrine that there are two independent principles, one good and the other evil.
c. Theol. The doctrine, attributed by his opponents to Nestorius, that Christ consisted of two personalities.
1794 MATHIAS Purs. Lit.  65 Then he introduces..the two principles or dualism (a little more French jargon) the monde animé and the monde machine. 1836-7 SIR W. HAMILTON Metaph. (1877) I. xvi. 293, I would be inclined to denominate those who implicitly acquiesce in the primitive duality as given in Consciousness, the Natural Realists or Natural Dualists, and their doctrine Natural Realism or Natural Dualism. 1847 BUCH tr. Hagenbach’s Hist. Doctr. I. 93 The Gnostic doctrine of two supreme beings (dualism). 1864 PUSEY Lect. Daniel (1865) 529 The characteristic error of the Zend religion, its Dualism, was its blot from the first. 1872 LIDDON Elem. Relig. iv. 148 Manicheeism was the Dualism which had acquired a Christian flavour by coming into contact with Christianity. 1882 FARRAR Early Chr. I. 263 The dualism the existence of matter as the source of evil apart from God finds a distinct expression in the Wisdom of Solomon. 1882-3 SCHAFF Encycl. Rel. Knowl. I. 669 According to dualism existence itself is based on a contrariety which appears in philosophy as spirit and matter.
4. Chem. The theory, originated by Berzelius, now abandoned, that every compound is constituted of two parts which have opposite electricities.
1884 MUIR Princ. Chem. I. ii. iii. §54 Dumas’ discovery of the chloracetic acids which marks the beginning of the revolt against the compound radicles of dualism.
You can see how much of a challenge and, really, how much fun it would be to define nondualism using the OED model. What’s the earliest use of the word nondualism? What quotations would you select? How about the words nondual, nondualist, nondualize, nonduality? They, too, would have to be defined in the same detail. Certainly there are fine quotations using those words.
And how about definitions for neo-nonduality? Neo-nondualist? Neo-nondualism? Or — I think I just invented a word — neo-nondualize?
Also see What Is Nonduality?