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The Collaborative International Dictionary
Near beer

Near beer \Near beer\ Any of various malt liquors (see Citation below).

Near beer is a term of common currency used to designate all that class of malt liquors which contain so little alcohol (usually less than 1/2 per cent) that they will not produce intoxication, though drunk to excess, and includes in its meaning all malt liquors which are not within the purview of the general prohibition law.
--Cambell v. City of Thomasville, Georgia Appeal Records, 6 212.

WordNet
near beer

n. drink that resembles beer but with less than 1/2 percent alcohol

Usage examples of "near beer".

Eyerack was so primitive in its military culture that they served real beer at the NCO club, instead of the recycled near beer at a real Trooper dive.