COLUMBIA, S.C.—While waiting for Bernie Sanders to speak at the University of South Carolina here on Tuesday, Andrew Zah, a college senior, could barely contain his enthusiasm. “He listens to everyone,” Zah said, standing in a buzzing overflow crowd of students waiting outside an auditorium long filled past capacity. “He gives everyone a voice.”

The context was very different, but the language strikingly similar later that afternoon when Donald Trump spoke in North Augusta, roughly 75 miles southwest of Columbia. About halfway through his speech, Trump summoned to the stage two men who had shouted down a lone Latino protester in the overwhelmingly white, heavily blue-collar audience.

Trump introduced one of them as a veteran of two tours in Iraq. The man instantly pivoted to thank Trump. “If it wasn’t for Mr. Trump right here,” he said, in a distant echo of Zah, “I don’t think any of us would have the voice we have.”

As those comments suggest, Sanders and Trump are rising largely because they are amplifying the voices of constituencies that have usually been outshouted in fights for their party’s nomination. For Trump, that key constituency is working-class Republicans; for Sanders, it’s the Millennial generation. By demonstrating—and crystallizing—these groups’ electoral clout, each man is signaling a lasting internal power shift in the party he is seeking to lead.

As the clear front-runner, Trump is drawing support from across the GOP as the critical South Carolina primary approaches on Saturday. But, from the start, his strength has been rooted in his extraordinary hold on Republicans without a college education. In the crowded New Hampshire primary, he won fully 42 percent of them, more than his next three closest competitors combined, according to exit polls.

Whites without a college degree, who began realigning away from the Democratic Party in the 1960s, are arguably now the GOP’s most important constituency. In every presidential election since 1996, they have provided 49 to 55 percent of the votes won by the GOP presidential nominee—even though non-college whites over that period have shrunk from about half of all voters to only about one-third. They played equally crucial roles in the 2008 and 2012 Republican presidential primaries, casting about half the votes.

Yet no GOP presidential contender more formidable than the conservative commentator Patrick J. Buchanan in 1996 or former Senator Rick Santorum in 2012, neither of whom came close to winning, has aimed his agenda squarely at those voters. In style and substance, John McCain and Mitt Romney, the 2008 and 2012 nominees, more represented the party’s managerial white-collar wing. Trump has decisively broken that pattern with a bristling, insular message that attacks both domestic elites and foreign influences, from Mexican immigrants to Chinese manufacturers.

The GOP’s blue-collar and white-collar factions agree on many issues. But polls show that working-class Republicans are both more nativist and statist: They are more likely to support temporarily banning Muslims from entering the U.S. and deporting all undocumented immigrants, and more hostile to free trade or cuts in federal entitlement programs for the elderly.

Trump embraces all of those positions—each of which conflicts with the views of most current party leaders, like House Speaker Paul Ryan. And Trump advances those views with a confrontational style that thrills his supporters—but alienates many upscale Republicans, who see him as erratic and un-presidential. These conflicts underscore how thoroughly a Trump nomination behind his platform of belligerent blue-collar populism would represent a hostile takeover of a party whose white-collar wing has usually picked its nominees.

Like Trump, Sanders is now drawing support from many different factions of his party. But his strength is also rooted in astronomical support among a single group: the Millennial generation. Both in Iowa and New Hampshire, Sanders carried over 80 percent of voters younger than 30, a head-spinning result. Millennials also gave strong support to Barack Obama in his 2008 race. But then they were supporting players behind the African Americans and white-collar whites who keyed Obama’s victory. History will likely record the Sanders campaign as the Millennial generation’s political coming out—much as the George McGovern’s 1972 campaign was for the baby boom.

The analogy is especially apt because Millennials are poised to eclipse the baby boom in influence. Millennials already represent one-third of Americans who identify as Democrats, a bigger portion than baby boomers, according to Pew Research Center polls. More broadly, Millennials now roughly equal baby boomers as a share of all eligible voters. As recently as 2008, boomers comprised nearly double the share of eligible voters as Millennials.

The Milllennials’ role in lifting Sanders ensures that Democrats will need to elevate their concerns, like mounting higher-education costs. (“Having to pay back all that student loan debt is, basically, impossible,” Satasade Roberts, a USC graduate student in social work, said outside Sanders’s event.) Sanders’s success at mobilizing so many Millennials into a movement to transform politics also shows that party leaders must develop strategies that touch their inclination toward inclusive, collective action. That won’t be easy, since Sanders’s inroads simultaneously demonstrate how many Millennials are willing to contemplate more fundamental liberal change than almost all Democratic leaders today consider feasible.

Republicans face a comparable challenge selling the party’s traditional agenda of small government at home and expansive internationalism abroad to the mostly economically-squeezed and culturally-aggrieved voters mobilized by Trump around precisely the opposite positions. Both sides may struggle to harmonize their current priorities and approaches with the soaring expectations of voters who feel that Sanders and Trump, for the first time, are providing them a voice.