The anti-establishment wave that propelled Donald Trump to the White House is developing into a political force that perhaps even the president cannot control and could shake his Republican Party ahead of next year's congressional elections.

That became clear on Tuesday night when Trump's favored candidate in an Alabama Senate primary, Luther Strange, was soundly defeated by Roy Moore, an arch-conservative who cast himself as an inheritor of Trump's insurgent mantle.

Moore's win is expected to encourage more outsider candidates to challenge Republican incumbents ahead of the November 2018 elections, where the party will seek to maintain its control of the Senate and House of Representatives, crucial to enacting Trump's agenda.