The OMJHL junior team took the name of the OHA senior team which had played for two years prior, which in themselves were named for Brantford's most famous former resident, telephone pioneer Alexander Graham Bell.

After two years in the OMJHL, the league changed names to the OHL and the Alexanders played four more seasons in Brantford, before moving back to Hamilton as the Steelhawks.

Brantford developed close rivalries with the London Knights and the Niagara Falls Flyers.

The Brantford Alexanders also had an official theme song recorded by County Line, called "Cowboys of the Ice".

In 1982–83, Dave Gagner was awarded the Bobby Smith Trophy for the OHA's Scholastic Player of the Year.