The Old Catholic Church affirms that Jesus declared Peter to be the rock upon which the church is built. Peter holds a foundational apostolic role and authority. However, Old Catholics explicitly reject the Roman doctrine of papal supremacy and papal infallibility.

Old Catholics affirm apostolic authority and succession but hold that Peter's authority is collegial and shared with other apostles, not monarchical or supreme. This maintains continuity with early patristic reading while rejecting medieval papal developments.