The Communion of Conciliar Catholic Churches is a Catholic denomination in full apostolic succession. There have always been other Catholic churches not under the jurisdiction of Rome since the beginning of the early church. Some of these include the Coptic Catholic Churches, the Armenian Catholics, the Orthodox Churches, and the Old Catholics, to name a few.
The Church was not always run by the clergy. In fact, it was always communal, with the principal role of the bishop to guard the faith, teach, pray, and oversee that the works of the community remain faithful to the Gospel, the Tradition, and the Sacraments. However, the Kings and Queens were the heads of the churches, particularly after Constantine united the Christian faith. As with all power, there always comes the propensity for abuse, and in Europe, the Medicis in the Middle Ages were very successful at transferring power from the kings and queens, to the bishops of Rome, who were being called "princes" of the church.
Conciliarism grew during the 13th and 14th centuries and was widely accepted through to the 15th century as a way to return the church to its ancient roots. Conciliarism, is defined by the New Catholic Encyclopedia [New York: McGraw-Hill, 1967] as a "doctrine asserting that a general council constitutes the supreme authority of the Church."
In the 18th century, the Roman Catholic church attempted to assert its supreme authority over all Catholics. It was a time when the Jesuits, wielding unprecedented political powers in the world principally due to the colonial conquests, attempted to gain even more power over the Catholic Churches.
They did this by interfering with the church in Holland and attempted to unlawfully depose the Archbishop of Utrecht. These believers also called a church council during a time of war when most of the bishops would not be able to attend. Vatican I was attended primarily by local Roman bishops, with little to no attendance by other Catholic bishops around the world. It is here where Rome splits from the rest of the church by attempting to claim her supremacy without the full attendance of the bishops. Here they proclaim a new, novel, and unprecedented concept of papal infallibility, where the bishop of Rome is declared the supreme voice of the church in faith and morals. Again, this was a novel and unprecedented concept to the church and one that was not agreed to by a majority of the bishops since most of them were unable to attend.
Many Catholics, especially in Germany, Austria, and Switzerland, disagreed with this action. While they agreed that the pope may be the head of the Roman Church, he was certainly not the head of the Church Catholic (i.e. the Church universal). He was not also “infallible,” as only Christ holds this position.
Infallibility has never been an authentic Catholic belief held be all the church at all times and in all places, nor was it ever a part of the teachings of Christ and of the apostolic tradition. The Old Catholics, faithful to the Archbishop of Utrecht, continued the apostolic succession in their churches and our bishops have our lines of succession through them.
Rome has declared time and again, and as of late in Dominus Iesus that the Old Catholics hold valid lines of succession. Therefore, they have a valid priesthood with sacraments, and since our lines of succession flow through them, we too have a valid priesthood and valid sacraments.