The Collaborative International Dictionary of English v.0.48:

Cyclic \Cyc"lic\ (s?k"l?k or s?"kl?k), Cyclical \Cyc"lic*al\
   (s?k"l?-kal), a. [Cf. F. cycluque, Gr. kykliko`s, fr. ky`klos
   See Cycle.]
   1. Of or pertaining to a cycle or circle; moving in cycles;
      as, cyclical time. --Coleridge.
      [1913 Webster]

   2. (Chemistry) Having atoms bonded to form a ring structure.
      Opposite of acyclic.

   Note: Used most commonly in respect to organic compounds.

   Note: [Narrower terms: bicyclic; heterocyclic;
         homocyclic, isocyclic]

   Syn: closed-chain, closed-ring.
        [WordNet 1.5]

   3. Recurring in cycles[2]; having a pattern that repeats at
      approximately equal intervals; periodic. Opposite of
      noncyclic.

   Note: [Narrower terms: alternate(prenominal),
         alternating(prenominal); alternate(prenominal), every
         other(prenominal), every second(prenominal);
         alternating(prenominal), oscillating(prenominal);
         biyearly; circadian exhibiting 24-hour
         periodicity); circular; daily, diurnal;
         fortnightly, biweekly; hourly; midweek,
         midweekly; seasonal; semestral, semestrial;
         semiannual, biannual, biyearly; semiweekly,
         biweekly; weekly; annual, yearly; biennial;
         bimonthly, bimestrial; half-hourly; half-yearly;
         monthly; tertian, alternate(prenominal);
         triennial]
         [WordNet 1.5]

   4. Marked by repeated cycles[2].
      [WordNet 1.5]

   Cyclic chorus, the chorus which performed the songs and
      dances of the dithyrambic odes at Athens, dancing round
      the altar of Bacchus in a circle.

   Cyclic poets, certain epic poets who followed Homer, and
      wrote merely on the Trojan war and its heroes; -- so
      called because keeping within the circle of a single
      subject. Also, any series or coterie of poets writing on
      one subject. --Milman.
      [1913 Webster]

WordNet (r) 3.0 (2006):

cyclical
    adj 1: recurring in cycles [syn: cyclic, cyclical] [ant:
           noncyclic, noncyclical]

Moby Thesaurus II by Grady Ward, 1.0:

115 Moby Thesaurus words for "cyclical":
   alternate, annular, annulate, annulose, articulated, atomatic,
   atomic, atomiferous, atomistic, beating, catenated, ceaseless,
   circinate, circling, circular, concatenated, connected, constant,
   continual, continued, continuing, continuous, coronary, crownlike,
   cyclic, cycloid, diatomic, dibasic, direct, discoid, disklike,
   endless, epochal, even, ever-recurring, every other, featureless,
   frequent, gapless, haunting, heteroatomic, heterocyclic, hexatomic,
   homocyclic, immediate, incessant, interminable, intermittent,
   isobaric, isochronal, isocyclic, isoteric, isotopic, joined,
   jointless, linked, measured, metronomic, monatomic, monotonous,
   never-ending, nonstop, oscillatory, pentatomic, perennial,
   periodic, periodical, pulsing, reappearing, reciprocal, recurrent,
   recurring, repetitive, returning, revenant, rhythmic, ring-shaped,
   ringlike, rotary, round, round-the-clock, rounded, running,
   seamless, seasonal, serial, serried, smooth, stable, steady,
   straight, subatomic, tetratomic, thematic, thick-coming, triatomic,
   tribasic, twenty-four-hour, ubiquitous, unbroken, unceasing,
   undifferentiated, undulant, undulatory, unending, uniform,
   unintermitted, unintermittent, unintermitting, uninterrupted,
   unrelieved, unremitting, unstopped, wavelike, wheeling