The Collaborative International Dictionary of English v.0.48:

Adherence \Ad*her"ence\, n. [Cf. F. adh['e]rence, LL.
   adhaerentia.]
   1. The quality or state of adhering.
      [1913 Webster]

   2. The state of being fixed in attachment; fidelity; steady
      attachment; adhesion; as, adherence to a party or to
      opinions.
      [1913 Webster]

   Syn: Adherence, Adhesion.

   Usage: These words, which were once freely interchanged, are
          now almost entirely separated. Adherence is no longer
          used to denote physical union, but is applied, to
          mental states or habits; as, a strict adherence to
          one's duty; close adherence to the argument, etc.
          Adhesion is now confined chiefly to the physical
          sense, except in the phrase "To give in one's adhesion
          to a cause or a party."
          [1913 Webster]

WordNet (r) 3.0 (2006):

adherence
    n 1: faithful support for a cause or political party or
         religion; "attachment to a formal agenda"; "adherence to a
         fat-free diet"; "the adhesion of Seville was decisive"
         [syn: attachment, adherence, adhesion]
    2: the property of sticking together (as of glue and wood) or
       the joining of surfaces of different composition; "the mutual
       adhesiveness of cells"; "a heated hydraulic press was
       required for adhesion" [syn: adhesiveness, adhesion,
       adherence, bond]

Moby Thesaurus II by Grady Ward, 1.0:

87 Moby Thesaurus words for "adherence":
   OK, acceptance, accordance, accretion, acquittal, acquittance,
   adhesion, admiration, agglomeration, agglutination, allegiance,
   approbation, approval, attachment, blessing, bona fides, bond,
   bonne foi, care, carrying out, cling, clinging, clotting,
   clustering, coagulation, coherence, cohesion, cohesiveness,
   compaction, compliance, concretion, condensation, conformance,
   conformity, congealment, congelation, conglobation, conglomeration,
   consolidation, constancy, countenance, devotedness, devotion,
   discharge, endorsement, esteem, execution, faith, faithfulness,
   favor, favorable vote, fealty, fidelity, firmness, fulfillment,
   good faith, heed, heeding, homage, inseparability, junction,
   keeping, loyalty, nod, observance, observation, performance,
   practice, respect, sanction, satisfaction, seal of approval, set,
   setting, solidification, stamp of approval, staunchness,
   steadfastness, sticking, tie, troth, true blue, trueness, voice,
   vote, yea, yea vote