The members of the mailers union voted last night to accept their contract, said Deborah Friedman, a spokeswoman for the union coalition.
"We are engaged in conversations with the union coalition and with other stakeholders to determine the next steps," said Rich Nelson, a United spokesman.
Two union coalitions that endured through the fiscal crisis - one for nonuniformed workers and the other for uniformed employees - have dissolved into separate negotiations.
It is common practice that seats are divided between representatives from the major union coalitions.
Hank Krakowski, a spokesman for the union coalition, said he envisioned ratification of the contracts within "a month or two at the extreme."
The employees' union coalition struggled to save the airline but failed.
Yesterday, United said that the "productive dialogue" with the union coalition was continuing and that it was still studying the coalition's proposal.
Despite the Teamsters' absence, the deal signifies a truce between two rival union coalitions that represent different sections of the railroad's work force.
The leaders of the union coalition were in a meeting and could not be reached for comment.
The union coalition hired investment bankers who predicted that losses would total about $100 million.