The Collaborative International Dictionary of English v.0.48:

Duteous \Du"te*ous\, a. [From Duty.]
   1. Fulfilling duty; dutiful; having the sentiments due to a
      superior, or to one to whom respect or service is owed;
      obedient; as, a duteous son or daughter.
      [1913 Webster]

   2. Subservient; obsequious.
      [1913 Webster]

            Duteous to the vices of thy mistress. --Shak.
      -- Du"te*ous*ly, adv. -- Du"te*ous*ness, n.
      [1913 Webster]