It is no wonder that the Apostle calls him beloved. Without doubt he was and remains beloved by all Christians who value his labors, both those accomplished during his life and those eternally active in his writings. He wrote them by the action of the Spirit of God, having diligently investigated all that he had seen and heard (Lk 1:1-2). One ancient interpreter says, Luke was beloved by St. Paul because, having left everything, he always followed this Apostle. The founding of the Church in Thebes of Boeotia is ascribed to Luke the Evangelist. There he died at eighty years of age. His memory is blessed on October 18.
Concerning Demas, the Apostle says nothing approving, since he probably saw nothing to approve. In the Second Epistle to Timothy, the Apostle writes that Demas had left him, having loved this present world (4:10).
Regarding the transmission of the greeting to the Laodiceans and to Nymphas, St. John Chrysostom observes: See how the Apostle brings them close and binds them to one another, not only by this kiss, but still more by afterwards commanding that the Epistle itself be sent to them for reading. Nymphas, one must suppose, was a presbyter who had taken the place of Epaphras. His whole household consisted of the faithful. Church assemblies were also held in his house, says Bishop Theophan.