The Collaborative International Dictionary of English v.0.48:

Illegitimacy \Il`le*git"i*ma*cy\, n.
   The state of being illegitimate. --Blackstone.
   [1913 Webster]

WordNet (r) 3.0 (2006):

illegitimacy
    n 1: the status of being born to parents who were not married
         [syn: bastardy, illegitimacy, bar sinister]
    2: unlawfulness by virtue of not being authorized by or in
       accordance with law [ant: legitimacy]