The Collaborative International Dictionary of English v.0.48:

Prevail \Pre*vail"\, v. i. [imp. & p. p. Prevailed; p. pr. &
   vb. n. Prevailing.] [F. pr['e]valoir, OF. prevaleir, L.
   praevalere; prae before + valere to be strong, able, or
   worth. See Valiant.]
   1. To overcome; to gain the victory or superiority; to gain
      the advantage; to have the upper hand, or the mastery; to
      succeed; -- sometimes with over or against.
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            When Moses held up his hand, Israel prevailed, and
            when he let down his hand, Amalek prevailed. --Ex.
                                                  xvii. 11.
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            So David prevailed over the Philistine. --1 Sam.
                                                  xvii. 50.
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            This kingdom could never prevail against the united
            power of England.                     --Swift.
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   2. To be in force; to have effect, power, or influence; to be
      predominant; to have currency or prevalence; to obtain;
      as, the practice prevails this day.
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            This custom makes the short-sighted bigots, and the
            warier skeptics, as far as it prevails. --Locke.
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   3. To persuade or induce; -- with on, upon, or with; as, I
      prevailedon him to wait.
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            He was prevailed with to restrain the Earl.
                                                  --Clarendon.
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            Prevail upon some judicious friend to be your
            constant hearer, and allow him the utmost freedom.
                                                  --Swift.
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The Collaborative International Dictionary of English v.0.48:

Prevailing \Pre*vail"ing\, a.
   1. Having superior force or influence; efficacious;
      persuasive. --Shak.
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            Saints shall assist thee with prevailing prayers.
                                                  --Rowe.
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   2. Predominant; prevalent; most general; as, the prevailing
      disease of a climate; a prevailing opinion.
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   Syn: Syn. See Prevalent.
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WordNet (r) 3.0 (2006):

prevailing
    adj 1: most frequent or common; "prevailing winds" [syn:
           prevailing, prevalent, predominant, dominant,
           rife]

Moby Thesaurus II by Grady Ward, 1.0:

174 Moby Thesaurus words for "prevailing":
   abounding, abundant, accidental, accompanying, accustomed, ado,
   affecting, affluent, afloat, afoot, all-sufficing, ample, aplenty,
   arch, ascendant, average, banner, besetting, bottomless, bounteous,
   bountiful, capital, cardinal, central, champion, chief,
   circumstantial, common, commonplace, conquering, conventional,
   copious, crowning, current, customary, defeating, diffuse, doing,
   dominant, dominating, effective, effectual, effuse, epidemic,
   eventuating, everyday, exhaustless, extravagant, exuberant,
   familiar, fat, fertile, first, flush, flushed with success, focal,
   forceful, foremost, full, galore, general, generous, going on,
   great, habitual, happening, headmost, hegemonic, household,
   in ascendancy, in hand, in plenty, in quantity, in the ascendant,
   in the wind, incidental, inexhaustible, influential, lavish,
   leading, liberal, luxuriant, magisterial, main, many, master,
   maximal, much, normal, normative, numerous, occasional, occurring,
   on, on foot, on the throne, ongoing, opulent, ordinary, overcoming,
   overflowing, overruling, pandemic, paramount, passing,
   plenitudinous, plenteous, plentiful, plenty, popular, potent,
   powerful, predominant, predominating, preeminent, prepollent,
   preponderant, prepotent, prescriptive, prevalent, primal, primary,
   prime, principal, prodigal, productive, profuse, profusive,
   rampant, ranking, regnant, regular, regulation, reigning, replete,
   resultant, rich, rife, riotous, routine, ruling, running,
   running over, sovereign, standard, star, stellar, stereotyped,
   stock, successful, superabundant, supereminent, swaying,
   taking place, teeming, telling, topflight, triumphal, triumphant,
   under way, universal, usual, vanquishing, vernacular, victorious,
   wealthy, well-found, well-furnished, well-provided, well-stocked,
   wholesale, widespread, winning, wonted