Graham Murray, 29, and Grant Murray, 19, appeared in private and face charges of carrying out the alleged attack on Jim Martin, 37.
SCOTSMAN TABLET AND MOBILE APPS
The men, both of Motherwell, Lanarkshire, made no plea or declaration at Hamilton Sheriff Court and were remanded in custody.
They face allegations they assaulted HGV driver Jim, of Newarthill, to his severe injury, danger of life and attempted to murder him on February 1.
Grant Murray faces further claims of assault and breach of the peace.
Both men are expected to appear at court for a second time on Friday.
Rangers fan Jim was treated in hospital after he was found injured outside a pub in his hometown just hours after he had watched Celtic beat Rangers 2-0 at Hampden Park.
His wife Laurette, 38, later released pictures of his injuries as she appealed for information.
Prosecutors have revealed a third man reported in connection with the incident has been released but could still be taken to court.
A Crown Office spokesman said: “The procurator fiscal received a report concerning a 24-year-old man in connection with an incident said to have occurred in Motherwell on February 1, 2015.
“After full and careful consideration of the facts and circumstances of the report, the accused was liberated from custody and did not appear in court in relation to this incident.
“The case remains under consideration by the procurator fiscal”.