Bernie Sanders defeated Hillary Clinton in the New Hampshire primary in every age group except people over sixty-five. PHOTOGRAPH BY SPENCER PLATT / GETTY

Let’s start with the qualifiers. New Hampshire is a small state tucked away in the northeast corner of the country, with a population that is, in many ways, unrepresentative of the United States as a whole. Compared to the rest of the country, it is whiter, quirkier, and more willing to turn its back on establishment candidates of both parties. Since 1988, no non-incumbent Democrat or Republican who has won a New Hampshire primary has gone on to win the Presidency.

All of that said, in the grand sweep of political history, what happened last night was remarkable. In the first primaries of the 2016 campaign, two candidates who are only barely members of their respective parties won the Democratic and Republican contests. And they didn’t just win. They* *trounced their opponents.

In the Democratic primary, Bernie Sanders, who once described himself as an independent socialist and now uses the term “democratic socialist,” won about sixty per cent of the vote. He defeated Hillary Clinton, who was long widely regarded as a shoo-in for the nomination, by more than twenty-one percentage points. In the Republican primary, Donald Trump, who calls himself a Republican but whose very name sends many longtime G.O.P. politicians and supporters into fits, got more than thirty-five per cent of the vote and defeated the second-place finisher, John Kasich, the governor of Ohio, by more than nineteen percentage points.

On the basis of recent opinion polls, which showed Sanders and Trump well ahead, these results weren’t entirely unexpected. But it is worth stepping back a bit. Nine months ago, when Sanders launched his campaign in New Hampshire, most political observers dismissed him as a fringe candidate. In June, when Trump entered the Republican race, most analysts, myself included, didn’t think he would go the distance. The pundits now stand embarrassed. The two New Yorkers—Sanders is from Brooklyn; Trump is from Queens—have campaigned as insurgents, each with a clear message. They rode to last night’s victories on a populist wave, the limits of which will determine the outcome of the primaries, and, quite possibly, the general election.

Unlike in the Iowa caucuses last week, there wasn’t much suspense about the outcomes. As soon as the last polls closed, at 8 P.M. Eastern, the Associated Press and the television networks called the races for Sanders and Trump, based on their exit polls. As the vote tallies came in, they broadly confirmed those poll numbers. The only close race was for third place on the G.O.P. side. In the early hours of Wednesday morning, with about ninety per cent of the vote counted, Ted Cruz was in third place, with 11.5 per cent of the vote, Jeb Bush was fourth, at 11.1 per cent, and Marco Rubio was in fifth, at 10.5 per cent.

At about nine P.M., CNN showed footage of Sanders shooting hoops in the gym at Concord High School, where his supporters had gathered to celebrate his victory. Half an hour later, after Clinton had delivered a feisty concession speech, Sanders took the stage, thanked the state, and delivered his standard stump address about how the economy and the political system are rigged to benefit wealthy campaign donors. Briefly, he also reflected on his victory, pointing out that it was based on a huge turnout—“and I say huge,” he repeated. We won, Sanders went on, “because we harnessed the energy and the excitement that the Democratic Party will need to succeed in November. . . . That will happen all over the country.”

As the campaign moves south and west, Sanders will face the challenge of making sure that it does happen. But, whatever takes place going forward, the breadth of his victory in New Hampshire was impressive. According to the network exit poll, he won the male vote by sixty-five per cent to thirty-four per cent, and the female vote by fifty-three per cent to forty-six per cent. Among women under the age of thirty, despite (or perhaps partly because of) the best efforts of Madeleine Albright and Gloria Steinem, he got eighty-two per cent of the vote.

Sanders won in every age group except people over sixty-five, and he came out ahead in every income group except those earning more than two hundred thousand dollars a year. The fact that he won by roughly two to one among voters earning less than fifty thousand dollars a year was especially notable. In 2008, low- and middle-income workers were at the core of Clinton’s campaign, and something similar was true in 1992, when Bill Clinton was elected President. On seeing the numbers, Larry Sabato, a veteran election watcher at the University of Virginia,* *tweeted, “No way Hillary can declare herself the comeback kid. The Clinton coalition from 1992 and 2008 has collapsed.”

Sanders ended his speech by appealing for campaign donations. He also evoked the memory of his parents, who lived in a three-room rent-controlled apartment, and declared, “On to Nevada, South Carolina, and beyond.”

Barely had he finished when, twenty minutes down I-93, in Manchester, Trump took the stage at his victory party and gave an equally characteristic performance. “Oh, wow!” he began. “Wow, wow, wow! So beautiful. So beautiful. We are going to make America great again.” Then Trump invoked his parents, who lived in an upscale housing development; thanked his campaign manager, Corey Lewandowski; and said, “You know, we learned a lot about ground games in one week.”

It is possible that Tuesday night will turn out to have represented the crest of the populist wave. Heading on from New Hampshire, the Clinton campaign will take solace from the fact that Sanders’s margin of victory was boosted by his forty-five-point lead among self-identified independents, who, according to the exit poll, made up almost* *forty per cent of the vote. In some other states, the electorate will be restricted to registered Democrats, and there will be a much bigger representation of non-whites—who, in New Hampshire, went to Clinton by four points, according to the exit poll.

With his opposition still divided, Trump is in a stronger position than Sanders. But, if the G.O.P. could ever settle on a candidate from the so-called establishment lane to challenge him, he could be in trouble. If you add up the votes cast for Kasich, Bush, Rubio, and Chris Christie (who came in sixth, with about eight per cent of the vote), it comes to about forty-five per cent, which is ten points more than Trump received. And Cruz, who will probably do well on Super Tuesday, can’t be entirely dismissed, either.

For now, though, the two boys from the outer boroughs are riding high. In battling their respective party establishments, they don’t generally have occasion to address one another directly. Trump’s victory speech did, however, include a concession that he’d seen some of “Bernie’s” spiel. He even asked the crowd to congratulate Sanders, which didn’t go down very well. “He wants to give away our country, folks,” Trump said, reverting to type. “We’re not going to let it happen.”

Sanders didn’t mention Trump, but he had his eye on their shared home town. After his speech, he flew to New York, where, today, he will appear on “The View” and the “Late Show with Steven Colbert.” With an eye to South Carolina and other states with many African-American voters, he was also reported to have a meeting planned with Al Sharpton.