One by one, Rep. Mike Capuano (D) is rounding up the backing of members of the state’s House delegation for his special election campaign for Massachusetts Senate.

The latest to formally endorse Capuano are two would-be primary rivals — 6th district Rep. John Tierney (D) and 9th district Rep. Stephen Lynch. Both men considered running for the seat, opened up by Sen. Edward Kennedy’s (D) death in August, before ultimately deciding to stand down. Tierney announced his support for Capuano on Sunday, and Lynch did so on Monday, both touting the work they’ve done in the House with Capuano, who has represented the Boston-area 8th district for six terms.

Also on board for Capuano are Reps. Barney Frank (D) and Jim McGovern (D). Capuano’s leading rival for the nomination, state Attorney General Martha Coakley (D), has not been endorsed by any of Massachusetts’ Members of Congress, but she has the backing of state Senate President Therese Murray (D) and state House Majority Leader James Vallee (D), as well as a slew of other state legislators.

Coakley and Capuano are also in a battle for labor union endorsements. On Friday, Coakley announced the endorsement of the Service Employees International Union State Council, which represents 60,000 members across the state.

Two other Democrats, Stephen Pagliuca, managing director of the financial firm Bain Capital and a co-owner of the NBA’s Boston Celtics, and Alan Khazei, co-founder of the City Year national volunteer program, are running as non-establishment candidates and are not expected to garner backing from many of the major Democratic constituency groups.

The primary in the special election is slated for Dec. 8 with the general election on Jan. 19. The Democratic nominee is favored to win over Republican candidate Scott Brown.