Last Tuesday’s Democratic primaries may have been the most significant New Haven has seen in a decade, but as some defeated candidates have made clear, this year’s political drama has only just begun.

When the dust from the primaries settled, many familiar characters in the city’s politics had been ousted — notably 20-year incumbent and Board of Aldermen President Carl Goldfield and, closer to home, Ward 22 Alderman Greg Morehead. But in a year when an unprecedented number of candidates have registered as independents for the general election, several who fell short among Democratic voters aim to try their luck again in November.

Rematches of this kind are set to take place across the city, but the one captivating the most attention is Jeffrey Kerekes’ battle to unseat 18-year incumbent Mayor John DeStefano Jr. While DeStefano won with a big margin Tuesday, he failed to earn a majority of Democrats’ support; 56 percent voted for one of his three challengers.

Kerekes, a budget watchdog and psychotherapist from Wooster Square who emerged this summer as the mayor’s sharpest critic, took the largest share of the votes that did not go to DeStefano with 22.4 percent. While Kerekes said he had hoped to win the primary, he knew from the beginning that his only realistic chance at defeating DeStefano would come in November.

“I needed to use the whole election cycle,” Kerekes said. “I couldn’t possibly do it just in the primary.”

The question that will likely decide the election is who will win over supporters of the two candidates who garnered less than 20 percent of the vote each — Tony Dawson and Clifton Graves — and who will not be on the ballot in November.

While rumors have surfaced among supporters of both Kerekes and the mayor about a potential endorsement of Kerekes by one or both candidates, Graves said he has not yet spoken to Dawson about the matter. A decision about whether and whom to endorse will likely be made next week, he said.

While an extended campaign season is certainly in store for the mayoral race, the aldermanic races in wards surrounding Yale run the gamut from dead to uncertain to very much alive.

In Dixwell’s Ward 22, which plays host to Morse, Stiles, Silliman and Timothy Dwight Colleges, four-year incumbent Morehead called it quits after Jeanette Morrison handily won Tuesday’s primary. With significant help from Yale students, many of whom worked on her campaign and helped shuttle other students to the polls Tuesday, Morrison took 359 votes to Morehead’s 196 including absentee ballots.

Morehead’s rationale for not pursuing a second chance in November as an independent boiled down to party loyalty.

“I’m not the type of person who jumps ship,” he said.

All three of his challengers in Tuesday’s primary, including Cordelia Thorpe and Lisa Hopkins, had registered as independents. Thorpe said she will be challenging Morrison in November, while Hopkins said she is still undecided.

It is not yet clear whether East Rock’s Ward 9 primary — a redux of a competitive 2010 special election to fill the seat of departing alderman Roland Lemar — was the last contest between incumbent Matt Smith ‘98 and Jessica Holmes. Just eight months after Smith edged Holmes by 48 votes, a surge in union support from unions representing Yale and city employees swept Holmes to victory along with 13 other candidates favored by unions.

Smith, who lost to Holmes by a vote of 325 to 455, said he is still unsure about whether to run against her in November.

Over in Dwight’s Ward 2, home to hundreds of Yalies living off campus, the drama is far from over. While street outreach worker Douglas Bethea earned less than half as many votes as Trumbull dining hall cook Frank Douglass, he said his campaign is just heating up.

“If I lose in November, I’ll go gracefully, but I’m not going down without a fight,” Bethea said.

Bethea said his primary motivation in contesting the general election is his fear that Douglass, a member of the executive board of Yale’s Local 35 and a recipient of financial backing from unions, will be beholden to a “union agenda” if elected alderman. While Douglass has emphatically rejected Bethea’s claim that there is a concerted effort by Yale and city unions to “take over the Board of Aldermen,” Bethea insisted his community’s representation in city government is under threat.

“When you knock on your alderman’s door, you want someone who will say ‘Sure, I can help you out with that,’ not ‘Hold on, I have to talk to my people,’” he said.

To most Yalies, the most relevant race this fall will be one that had no preliminary round last week: the race for Ward 1 alderman. Vinay Nayak ’14 and Sarah Eidelson ’12 have begun campaigning for the seat, currently held by Mike Jones ’11, who is not seeking re-election. Whatever the outcome of that contest, a competitive general election in Ward 1, home to Old Campus and eight residential colleges, will bring Yalies out to the polls in greater numbers than last Tuesday’s mayoral primary, in which just 48 voters cast ballots.