Apostolic succession is the tracing of a direct line of apostolic ordination, Orthodox doctrine, and full communion from the Apostles to the current episcopacy of the Orthodox Church. All three elements are constitutive of apostolic succession.
It is through apostolic succession that the Orthodox Christian Church is the spiritual successor to the original body of believers in Christ that was composed of the Apostles. This succession manifests itself through the unbroken succession of its bishops back to the apostles.
The unbrokenness of apostolic succession is significant because of Jesus Christ's promise that the "gates of hell" (Matthew 16:18) would not prevail against the Church, and his promise that he himself would be with the apostles to "the end of the age" (Matthew 28:20). According to this interpretation, a complete disruption or end of such apostolic succession would mean that these promises were not kept as would an apostolic succession which, while formally intact, completely abandoned the teachings of the Apostles and their immediate successors; as, for example, if all the bishops of the world agreed to abrogate the Nicene Creed or repudiate the Holy Scripture.
Orthodox teachings today are the same as that of the first apostles, though their mode of expression has adapted over the centuries to deal with heresies, changes in culture and so forth. This form of the doctrine was first formulated by St. Irenaeus of Lyons in the second century, in response to certain Gnostics. These Gnostics claimed that Christ or the Apostles passed on some teachings secretly, or that there were some secret apostles, and that they (the Gnostics) were passing on these otherwise secret teachings. Irenaeus responded that the identity of the original Apostles was well known, as was the main content of their teaching and the identity of the Apostles' successors. Therefore, anyone teaching something contrary to what was known to be apostolic teaching was not, in any sense, a successor to the Apostles or to Christ.
In addition to a line of historic transmission, Orthodox Christian churches additionally require that a hierarch maintain Orthodox doctrine as well as full communion with other Orthodox bishops. As such, the Orthodox do not recognize the existence of apostolic succession outside the Orthodox Church, precisely because the episcopacy is a ministry within the Church.
Apostolic succession in the Holy Scriptures
Most theologians of the protestant tradition deny the doctrine of apostolic succession and are ardant believers of congregationalism. Consider this statement from a protestant website: "nowhere in Scripture did Jesus, the apostles, or any other New Testament writer set forth the idea of 'apostolic succession'" . To refute this clearly anti-orthodox statement, one must merely point to the testimony of the New Testament, especially The Acts of the Apostles.
No one else dared join them, even though they were highly regarded by the people. Acts 5:13 (Note: this shows that the early Christians had a reverence for them)
We have heard that some went out from us without our authorization and disturbed you, troubling your minds by what they said. Acts 15:24
As they traveled from town to town, they delivered the decisions reached by the apostles and elders in Jerusalem for the people to obey. Acts 16:4
For we are not like many, peddling the word of God, but as from sincerity, but as from God, we speak in Christ in the sight of God. 2 Corinthians 2:17 (Note: this shows that the office they hold is more then self appointed authority).
having been built on the foundation of the apostles and prophets, Christ Jesus Himself being the corner stone Eph. 2:20 (Note: the word founation is used to describe "the apostles and prophets", not just St. Peter)
Keep watch over yourselves and all the flock of which the Holy Spirit has made you overseers. Be shepherds of the church of God, which he bought with his own blood. Acts 20:28 (Note: this is a clear testimony that the Holy Spirit appointed the Twelve to be "oeverseers" and "shepherds of the church")
As you sent me into the world, I have sent them into the world. John 17:18 (Note: the Bible compares the ministry of Jesus to that of the Twelve)
Transfer of Apostolic Authority Via the Holy Mystery of Ordination
Paul and Barnabas appointed elders for them in each church and, with prayer and fasting, committed them to the Lord, in whom they had put their trust. Acts 14:23
17 Then Ananias went to the house and entered it. Placing his hands on Saul, he said, "Brother Saul, the Lord—Jesus, who appeared to you on the road as you were coming here—has sent me so that you may see again and be filled with the Holy Spirit." 18 Immediately, something like scales fell from Saul's eyes, and he could see again. He got up and was baptized, 19 and after taking some food, he regained his strength. Acts 9:17-19 (Note: God sent Ananias to Paul so that he may lay hand upon him. Only after this point does Paul have the authority to minister)
3"Therefore, brethren, select from among you seven men of good reputation, full of the Spirit and of wisdom, whom we may put in charge of this task. 4 "But we will devote ourselves to prayer and to the ministry of the word." 5 The statement found approval with the whole congregation; and they chose Stephen, a man full of faith and of the Holy Spirit, and Philip, Prochorus, Nicanor, Timon, Parmenas and Nicolas, a proselyte from Antioch. 6 And these they brought before the apostles; and after praying, they laid their hands on them. Acts 6:3-6 (Note: A clear instance of Ordination)
1 I charge you in the presence of God and of Christ Jesus, who is to judge the living and the dead, and by his appearing and his kingdom: 2 preach the word; be ready in season and out of season; reprove, rebuke, and exhort, with complete patience and teaching. 3 For the time is coming when people will not endure sound teaching, but having itching ears they will accumulate for themselves teachers to suit their own passions, 4 and will turn away from listening to the truth and wander off into myths. 5 As for you, always be sober-minded, endure suffering, do the work of an evangelist, fulfill your ministry. 6 For I am already being poured out as a drink offering, and the time of my departure has come. 2 Tim. 4:1-6 (St. Paul hands down his minidtry to Timothy)
For this reason I remind you to kindle afresh the gift of God which is in you through the laying on of my hands. 2 Tim. 1:6 (Note: Paul reminds Timothy of the gift he received through laying of hands)
Do not neglect the spiritual gift within you, which was bestowed on you through prophetic utterance with the laying on of hands by the presbytery. 1 Tim. 4:14 (Note: This shows that divine authority is bestowed unto someone using laying on of hands)
15 In those days Peter stood up among the believers(a group numbering about a hundred and twenty) 16 and said, "Brothers, the Scripture had to be fulfilled which the Holy Spirit spoke long ago through the mouth of David concerning Judas, who served as guide for those who arrested Jesus— 17 he was one of our number and shared in this ministry." 18(With the reward he got for his wickedness, Judas bought a field; there he fell headlong, his body burst open and all his intestines spilled out. 19 everyone in Jerusalem heard about this, so they called that field in their language Akeldama, that is, Field of Blood.) 20 "For," said Peter, "it is written in the book of Psalms, " 'May his place be deserted; let there be no one to dwell in it,' and, " 'May another take his place of leadership.' 21 Therefore it is necessary to choose one of the men who have been with us the whole time the Lord Jesus went in and out among us, 22 beginning from John's baptism to the time when Jesus was taken up from us. For one of these must become a witness with us of his resurrection." 23 So they proposed two men: Joseph called Barsabbas (also known as Justus) and Matthias. 24 Then they prayed, "Lord, you know everyone's heart. Show us which of these two you have chosen 25 to take over this apostolic ministry, which Judas left to go where he belongs." 26 Then they cast lots, and the lot fell to Matthias; so he was added to the eleven apostles. Acts 1:15-26