The Collaborative International Dictionary of English v.0.48:

Apostolic \Ap`os*tol"ic\, Apostolical \Ap`os*tol"ic*al\, a. [L.
   apostolicus, Gr. ?: cf. F. apostolique.]
   1. Pertaining to an apostle, or to the apostles, their times,
      or their peculiar spirit; as, an apostolical mission; the
      apostolic age.
      [1913 Webster]

   2. According to the doctrines of the apostles; delivered or
      taught by the apostles; as, apostolic faith or practice.
      [1913 Webster]

   3. Of or pertaining to the pope or the papacy; papal.
      [1913 Webster]

   Apostolical brief. See under Brief.

   Apostolic canons, a collection of rules and precepts
      relating to the duty of Christians, and particularly to
      the ceremonies and discipline of the church in the second
      and third centuries.

   Apostolic church, the Christian church; -- so called on
      account of its apostolic foundation, doctrine, and order.
      The churches of Rome, Alexandria, Antioch, and Jerusalem
      were called apostolic churches.

   Apostolic constitutions, directions of a nature similar to
      the apostolic canons, and perhaps compiled by the same
      authors or author.

   Apostolic fathers, early Christian writers, who were born
      in the first century, and thus touched on the age of the
      apostles. They were Polycarp, Clement, Ignatius, and
      Hermas; to these Barnabas has sometimes been added.

   Apostolic king (or majesty), a title granted by the pope
      to the kings of Hungary on account of the extensive
      propagation of Christianity by St. Stephen, the founder of
      the royal line. It is now a title of the emperor of
      Austria in right of the throne of Hungary.

   Apostolic see, a see founded and governed by an apostle;
      specifically, the Church of Rome; -- so called because, in
      the Roman Catholic belief, the pope is the successor of
      St. Peter, the prince of the apostles, and the only
      apostle who has successors in the apostolic office.

   Apostolical succession, the regular and uninterrupted
      transmission of ministerial authority by a succession of
      bishops from the apostles to any subsequent period.
      --Hook.
      [1913 Webster]

WordNet (r) 3.0 (2006):

apostolical
    adj 1: proceeding from or ordered by or subject to a pope or the
           papacy regarded as the successor of the Apostles; "papal
           dispensation" [syn: papal, apostolic, apostolical,
           pontifical]
    2: of or relating to or deriving from the Apostles or their
       teachings [syn: apostolic, apostolical]