There are some groups from the Eastern Catholic churches that are recognized, and in communion with Rome, but for much of the Eastern Orthodox churches this is not the case, and the issue of apostolic succession is a sticking point on full communion.

From this link I will paste what is most likely the complete answer.  There are some Episcopalean churches that have left their faith and converted to be Catholic, and those priests are allowed to be married, but they are now in communion.

But, for any head of the church (the Pope) the RCC only recognizes the current Pope as being the successor of Peter, no other leader is seen as having that mantle.

[Catholic Answers](http://forums.catholic.com/showthread.php?t=421289)

> The Eastern Catholics are the 22 Churches sui iuris that are in full
> communion with the pope, and act as part of the synod of the Catholic
> Church, while retaining self governing status as churches, called
> Churches Sui Iuris.
> 
> Byzantine Rite Catholics and Greek Catholics (14 churches sui iuris)
> (the terms are synonyms, as is Greek Rite Catholic) are generally
> portions of the Eastern Orthodox Churches which left the Eastern
> Orthodox communion and joined the Catholic Communion. 1 has no
> orthodox counterpart (Italo-Albanian GCC), 1 has an orthodox
> counterpart that is a schism from the Catholic (The ACROD split from
> the Ruthenian GCC); the rest have parallels from the time of their
> split. Two have no hierarchs (Russian and one other).
> 
> Other Eastern Catholics (7 churches sui iuris) are of other Eastern
> Rites, and most have non-Catholic Parallel churches. Some, the
> majority synod is the Catholic; others the majority synod is the
> non-catholic.
> 
> The Chaldeans (Catholic Communion) are parallel to the Assyrian Church
> of the East (Oriental Orthodox Communion)
> 
> The Syro-Malabar and Syro-Malankar Catholic Churches have parallel
> Syriac churches and protestant churches using the same liturgical
> rites.
> 
> The Syrian Catholic and Syrian Orthodox churches parallel.
> 
> The Coptic Catholic Church split off from the Coptic Orthodox Church.
> 
> The Ethiopian Catholic Church parallels the Ethiopian Tehwado Orthodox
> and the Eritrean Orthodox. 
> 
> The Armenian Catholics and the Armenian Apostolic Orthodox have an
> unusual relationship; the Armenian Catholics are in full communion
> with the other Catholic Churches, but are, as a practical matter,
> still in communion with their parent Armenian Apostolic Orthodox.
> Deacons assisting across church boundaries are common; priestly
> concelebration happens with patriarchal tacit approval. Hierarchical
> concelebration doesn't seem to happen... 
> 
> The Maronite Catholics have no parallel church.

  [1]: http://forums.catholic.com/showthread.php?t=421289