BEDFORD, N.H. — After a bruising New Hampshire primary that saw wide victory margins, both parties head to South Carolina and Nevada conflicted about their presidential front-runners and facing nominating contests that could stretch for months.

The crushing victories by billionaire Donald Trump over his Republican challengers and by Senator Bernie Sanders of Vermont over former secretary of state Hillary Clinton on the Democratic side served as clear rebukes to each party’s establishment, as candidates with more traditional resumes finished far behind them. The results sow even more deeply the uncertainty about the parties’ trajectories.

After finishing far back in the pack, Governor Chris Christie of New Jersey and former Hewlett-Packard chief executive Carly Fiorina both suspended their campaigns Wednesday, further thinning what was once a vast GOP field.

Also Wednesday afternoon, Sanders’ campaign announced it had raised $5.2 million in the 18 hours since the last polls in New Hampshire closed, a formidable sum that signals the self-described democratic socialist’s durability.

Both races now shift south and west. Republicans vote next on Feb. 20 in South Carolina, a state both more conservative and more ideologically diverse than New Hampshire. The same day, Democrats hold caucuses in Nevada.

From there, the parties flip, with GOP caucuses in Nevada on Feb. 23 and the Democratic primary in South Carolina on Feb. 27. On March 1, known as “Super Tuesday,’’ voters in 13 states, including those from both parties in Massachusetts, will make their picks.

“People are starting to pay attention,’’ Governor John Kasich of Ohio said in Charleston, S.C., on Wednesday, after a strong second-place finish in New Hampshire. “And they’re either going to like me or they’re not.’’

Christie, who staked much of his remaining political capital on New Hampshire, picked up the support of Massachusetts Governor Charlie Baker last Friday. But Christie still finished a distant sixth on Tuesday.

Perhaps his most lasting imprint on the race will be the damage Christie inflicted to Senator Marco Rubio of Florida in Saturday’s debate. Rubio had claimed momentum from a third-place finish in Iowa, but Christie focused much of his energy on denting the first-term senator in New Hampshire.

Sanders has trailed Clinton by double digits in polling in the next states to vote, but backers are hoping his New Hampshire victory can turn that tide.

“There’s a sense that the inevitability factor’s gone,’’ said former South Carolina Democratic party chairman Dick Harpootlian, who backed Bill Clinton in 1992 but went with Barack Obama in 2008 and this year is supporting Sanders.

After the initial flush of early campaigning in Iowa and New Hampshire, the primary now shifts to states where the candidates have spent significantly less time. In South Carolina and Nevada, the electorates are also more diverse than the largely white first two states.

In South Carolina, former Florida governor Jeb Bush is leaning heavily on his family name in hopes to convert his fourth-place finish in New Hampshire into momentum. The campaign on Wednesday released a radio ad featuring former President George W. Bush endorsing his brother.

Sanders, whose win over Clinton outpaced expectations, also moved swiftly to shore up his support among the Democratic base. On Wednesday, he met the Rev. Al Sharpton in Harlem, an overture to African-American voters.

Both parties appear headed for historically unpredictable primaries, voters in both bases having soured on the chosen candidates of their respective party’s establishments.

In every election since 1968, Republicans have nominated a candidate who placed first in either Iowa or New Hampshire. Senator Ted Cruz placed first in the Iowa caucuses and third in the New Hampshire primary. Trump placed second in the caucuses and first in the primary.

But both men are antithetical to the GOP establishment in policy disagreements and personal style. But mainstream Republicans remain divided over which candidate to back as an alternative.

Kasich banked much of his bid on New Hampshire, and secured second place here by a healthy margin. But he has heavy competition for like-minded voters, including from Bush and Rubio, and critics say his campaign is ill-equipped to thrive in states further down the electoral calendar.

On the Democratic side, two states have now voiced skepticism about Clinton’s candidacy.

She also faces doubts about her trustworthiness: Exit polls here show that Sanders won about nine of 10 voters who said honesty was important to them.

Sanders won voters of both genders and, as in Iowa, dominated among younger voters, winning among those under 30 by a margin of 84 percent to 15 percent, according to exit polls.

But Sanders is now moving onto safer territory for Clinton, where her family’s long history with party powerbrokers can provide an advantage and where Sanders’ relatively new national brand remains unknown.

Jim O’Sullivan can be reached at jim.osullivan@globe.com. Follow him on Twitter at @JOSreports.