Union leaders representing employees of a Ronkonkoma-based school bus company have set a membership vote for Oct. 17 on the company's most recent contract offer.

The vote could trigger an immediate strike affecting about 35 districts that contract with Baumann & Sons Buses Inc. and its affiliate, Acme Buses, for all or part of their transportation. About 15,000 students in Nassau and Suffolk counties could find themselves without a ride.

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If Bauman doesn't change its position "on a number of issues, we will strongly recommend that you reject" the offer "and call for an immediate strike," Timothy Lynch, president of Teamsters Local 1205, said in a Friday letter to 1,200 union members.

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Lynch said details of the company's most recent offer would be discussed before a secret ballot vote at the 10 a.m. membership meeting in Hauppauge. There is at least one negotiating session planned for next week, and the union is open to more, he said. "There are still a number of very central issues on which the company's positions are completely unacceptable," Lynch told members.

A Baumann representative said in an email Friday night the company is "very confident that there will not be any good reason for anyone to strike over any differences that may exist in the parties' positions."

Baumann has criticized the union as being inflexible, while the company made a number of concessions during talks with a federal mediator. The dispute between the union and Baumann began this summer. In August, the union sent out a letter notifying dozens of Long Island school districts that contract with the company about the likelihood of a strike. The contract expired in June.

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Children most likely to be affected are special needs and special education students, who typically use smaller buses and vans, which company officials said make up an estimated 80 percent of its fleet of 1,100 buses.