κατὰ τὸν αὐτὸν καιρόν. The κατὰ allows some margin in time and does not necessarily imply the same day. Dionysius is the first one to connect the deaths of Peter and Paul chronologically, but later it became quite the custom. One tradition put their deaths on the same day, one year apart (Augustine and Prudentius, e.g., are said to support this tradition). Jerome (de vir. ill. 1) is the first to state explicitly that they suffered on the same day. Eusebius in his Chron. (Armen.) puts their martyrdom in 67, Jerome in 68. The Roman Catholic Church celebrates the death of Peter on the 29th and that of Paul on the 30th of June, but has no fixed tradition as to the year of the death of either of them.