More than 70 autistic children are on a waiting list to get support in Bradford schools because a specialist service is so stretched.
Janet Taylor, head of the service, told a Bradford Council inquiry into school funding it had "severe budgeting issues".
And Mrs Taylor, the headteacher of Greenfield Special School in Idle, said special schools needed the funding formula required to recognise very challenging pupils, such as one who broke the jaw of a teacher at her school.
Mrs Taylor was giving evidence at a session for the public as part of the six-day hearing.
She said the service for children with autism, which supports them in mainstream schools, dealt with 24 children in 1994 but now helps more than 200.
"Since 1996 we have been writing to the local education authority saying we cannot support these children," she said. "Today there is a waiting list of more than 70."
She said the youngsters had a high level of need but the teachers were not available to support them.
Mrs Taylor said the situation was made worse by the loss of a full-time post last year, meaning 49 children had to be transferred to another teacher - 19 of these had to go back on the waiting list.
She told the Council's overview and scrutiny committee that in 1990 her school had four children with autism and now 84 per cent of the 52 pupils had an autistic spectrum disorder.
This was not down to better diagnosis, she said, as their conditions were obvious.
Mrs Taylor said funding for special schools had to be increased or several would be in deficit by next year.
She said the way needs were assessed should to be changed to take account of very complex children so more funding was given to support them.
Giving examples of challenging youngsters, Mrs Taylor said sometimes three staff members were needed to deal with one child.
"Another child who came to us from another special school because it could not meet his needs broke the jaw of a member of staff. We have staff who are in the front line of severe aggression and violence on a daily basis."
Chris George, chairman of governors at Cullingworth Primary School, spoke about the difficulties of balancing the books.
The school's finance committee had to allocate cash for fixed costs, such as teachers, instead of deciding what to do with any funding left over.
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