Councils of Carthage
The Councils of Carthage were a series of councils held in north Africa in the city of Carthage by the Church of Africa during the third through fifth centuries. During these centuries the Church in Carthage rejected the claim of the Bishop of Rome to appellate jurisdiction. After the subjection, first, by the Vandals in the fifth century then followed by the Muslim Arabs in the seventh and eighth centuries Church of the former Roman province of Africa was largely destroyed.
Councils of the third century
Council of 251
Assembled under the presidency of bishop Cyprian of Carthage, a synod met in Carthage during May 251 to consider the treatment of those who apostatized during persecution, termed lapsi, and of Felicissimus and five other Novation bishops who had been excommunicated for usurping St. Cyprian's authority during the Decian persecution of 250. The synod declared that the lapsi should be dealt with in accordance with the degree of individual guilt and not with indiscriminate severity and affirmed the excommunication. These decisions were confirmed by a synod in Rome in the autumn of the same year. Felicissimus and his followers attempted to have their case re-opened in the following year, but their demands were rejected.
The council also declared that baptisms outside the Church, that is by heretics, were not valid and for those who were "baptized" by heretics a baptism was required for entry into the Church. The council also forbade re-baptism of those who had received baptism within the Church, but who sought readmission after having fallen into heresy. Another council was held in Carthage concerning the lapsi in 254.
Council of 252
The council of 252, under the presidency of Bp. Cyprian, established lower requirements for readmission to communion for those who showed serious penance and reaffirmed the decisions concerning baptism that were made at the year earlier council.
Council of 255
Actually a series of three meetings under Cyprian that pronounced against the validity of heretical baptism. An initial council in 255, followed by another in 256, pronounced against their validity which took direct issue with Stephen I of Rome who quickly repudiated the decisions. Rome at that time considered baptisms by heretics as valid. A third meeting in September 256 unanimously reaffirmed the position of the two earlier meetings. The pretensions by Bp. Stephen of authority over the bishops of Africa were strongly resented by the African bishops, a situation that severely strained relations between the Roman and African Sees.
Councils of the fourth century
Council of 348
About the year 348, the Orthodox bishops of Carthage met to memorialize their gratitude for the effective official repression of the Donatists, declared against the re-baptism of any one who had been baptized in the name of the Holy Trinity, and adopted twelve canons of clerical discipline.
Council of 397
On August 28, 397, a Council of Carthage, numbered the third by Denzinger,  issued a canon of the Holy Scripture quoted as including, "Genesis, Exodus, Leviticus, Numbers, Deuteronomy, Joshua son of Nun, Judges, Ruth, 4 books of Kingdoms, 2 books of Chronicles, Job, the Davidic Psalter, 5 books of Solomon, 12 books of Prophets, Isaiah, Jeremiah, Daniel, Ezekiel, Tobias, Judith, Esther, 2 books of Ezra, 2 books of Maccabees, and in the New Testament: 4 books of Gospels, 1 book of Acts of the Apostles, 13 letters of the Apostle Paul, 1 letter of his to the Hebrews, 2 of Peter, 3 of John, 1 of James, 1 of Jude, and one book of the Apocalypse of John." 
Councils of the fifth century
Council of 411
An assembly presided over by Marcellinus of Carthage that, under the direction of emperor Honorius, decreed Donatism heretical and demanded that the Donatists surrender their churches. This action led to the violent suppression of the Donatists.
Council of 418
A council convened on May 1, 418 under the presidency of Bishop Aurelius of Carthage that took action against the errors of Caelestius, a disciple of Pelegius. The council denounced the Peligian doctrines concerning human nature, original sin, grace, and perfectibility. The council also established regulations for clergy that included excommunication for clerics lower than bishop who appealed decisions outside of Africa, thus denying jurisdiction of the bishop of Rome in African church.
Councils of 419 and 424
These councils continued the dispute between the Churches of Carthage and Rome concerning appeals to Rome. The council of 424 addressed a letter to the Bishop Celestine of Rome, protesting against his claim to appellate jurisdiction, urgently requesting the immediate recall of his legate, and advising him to send no more judges to Africa. Bp. Celestine refused, citing the see's apostolic authority.
- Hefele, 2nd ed., i. Section 6, pp. 117-119 (English translation, i. pp. 99 sqq.); Mansi, i. pp. 921 sqq., 951 sqq.; Hardouin, i. pp. 153 sqq.; Cyprian, Epp. 69-75.
- Denzinger 186 in the new numbering, 92 in the old
- McDonald & Sanders' The Canon Debate, Appendix D-2, note 19: Revelation was added later in 419 at the subsequent synod of Carthage."
- Hefele, 2nd ed., ii. pp. 120 sqq., 137 sqq. (English translation, ii. pp. 462 sqq., 480 sqq.); Mansi, iii. pp. 835 sqq., iv. pp. 401 sqq., 477 sqq.; Hardodin, i. pp. 943 sqq., 1241 sqq. (L F. C.)