The Collaborative International Dictionary of English v.0.48:

Next \Next\ (n[e^]kst), a., superl. of Nigh. [AS. n[=e]hst,
   ni['e]hst, n[=y]hst, superl. of ne['a]h nigh. See Nigh.]
   1. Nearest in place; having no similar object intervening.
      --Chaucer.
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            Her princely guest
            Was next her side; in order sat the rest. --Dryden.
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            Fear followed me so hard, that I fled the next way.
                                                  --Bunyan.
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   2. Nearest in time; as, the next day or hour.
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   3. Adjoining in a series; immediately preceding or following
      in order.
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            None could tell whose turn should be the next.
                                                  --Gay.
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   4. Nearest in degree, quality, rank, right, or relation; as,
      the next heir was an infant.
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            The man is near of kin unto us, one of our next
            kinsmen.                              --Ruth ii. 20.
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   Note: Next is usually followed by to before an object, but to
         is sometimes omitted. In such cases next in considered
         by many grammarians as a preposition.
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   Next friend (Law), one who represents an infant, a married
      woman, or any person who can not appear sui juris, in a
      suit at law.
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The Collaborative International Dictionary of English v.0.48:

Next \Next\, adv.
   In the time, place, or order nearest or immediately
   succeeding; as, this man follows next.
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The Collaborative International Dictionary of English v.0.48:

Nigh \Nigh\ (n[imac]), a. [Compar. Nigher (n[imac]"[~e]r);
   superl. Nighest, or Next (n[e^]kst).] [OE. nigh, neigh,
   neih, AS. ne['a]h, n[=e]h; akin to D. na, adv., OS. n[=a]h,
   a., OHG. n[=a]h, G. nah, a., nach to, after, Icel. n[=a] (in
   comp.) nigh, Goth. n[=e]hw, n[=e]hwa, adv., nigh. Cf. Near,
   Neighbor, Next.]
   1. Not distant or remote in place or time; near.
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            The loud tumult shows the battle nigh. --Prior.
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   2. Not remote in degree, kindred, circumstances, etc.;
      closely allied; intimate. "Nigh kinsmen." --Knolles.
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            Ye . . . are made nigh by the blood of Christ.
                                                  --Eph. ii. 13.
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   Syn: Near; close; adjacent; contiguous; present; neighboring.
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WordNet (r) 3.0 (2006):

next
    adv 1: at the time or occasion immediately following; "next the
           doctor examined his back"
    adj 1: immediately following in time or order; "the following
           day"; "next in line"; "the next president"; "the next
           item on the list" [syn: following, next]
    2: nearest in space or position; immediately adjoining without
       intervening space; "had adjacent rooms"; "in the next room";
       "the person sitting next to me"; "our rooms were side by
       side" [syn: adjacent, next, side by side(p)]
    3: (of elected officers) elected but not yet serving; "our next
       president" [syn: future(a), next, succeeding(a)]