SacredHeartFan, i feel like lots of people brought up points that could confuse someone who is unfamiliar with Eastern Christianity, so i want to address some of those.
First, the Pope of Alexandria: The Bishop of Alexandria (who is the successor of St. Mark in the same way the Bishop of Rome is the successor of St. Peter, and the Bishop of Constantinople that of St. Andrew) is the Patrarich of the Coptic Orthodox Church, the remnant of Christian Egypt before the Islamic Arab invasions. The Patriarch of Alexander uses the title “pope,” meaning “father.” It is an honorific title; it does not mean that the Copts “have their own pope” to replace Rome’s. It just means that Copts and Romans ended up using the same honorary title. Either could easily be called something else without changing who they are or what they do. In fact, the Pope of Alexandria used the title far earlier than the Pope of Rome did.
On Eastern Priests concelebrating with Latins: As others have said, Eastern Orthodox clergy cannot concelebrate the Divine Liturgy (which is, of course, called “Mass” by us Roman Catholics) with Catholic clergy. The two churches are not in full communion. However, as the two churches continue to become closer, lots of times Orthodox and Catholic clergy will be guests at each others’ liturgies. Pope Benedict and Patriarch Bartholomew have brought this to a new level of visibility and pomp.
However, what you probably saw were Eastern Catholics, who are those Eastern or Oriental Christians who either never split away from Rome, or who returned to full communion after a schism. There is a group of Eastern Catholics for pretty much every type of Eastern Church not in communion with Rome. There are many Byzantine Catholics who celebrate the same liturgy, the same feast days, and wear the same vestments as the Eastern (Greek/Russian/etc) Orthodox. There are Coptic Catholics who celebrate identically to the Coptic Orthodox. There are Chaldean Catholics who celebrate pretty much identically to the Assyrian Christians.
Remember, the Catholic Church is made up of MANY churches in communion with the Bishop of Rome. The Roman Church is just one of many, 23 to be exact. Many have different heritages, rituals, and ways of expression Catholic beliefs. Any member of ONE of those churches can receive the sacraments from any other. So you could, for instance, go to Ukrain, and go to a Ukrainian Orthodox Church, and you could not receive the Eucharist because the Orthodox are not in full Communion with Rome. However, you could walk across the street to a Ukrainian Catholic church, where the liturgy would be identical in every way (except they pray for the Pope) and receive the Eucharist, because they are in full comunion with Rome.
If you see an Eastern Christian and a Western (Latin) Christian celebrating liturgy together, then the Eastern Christian is Eastern Catholic, not Eastern Orthodox.