TORIES have raised concerns over a multi-million pound Private Finance Initiative between Kirklees Council and builders Jarvis.
Their fears follow news of the troubled firm's mounting debts.
Jarvis has a £50m deal with the council to renovate 20 schools.
A second contract is being planned for the £25m construction of four new special schools.
Kirklees Tory group leader Clr Robert Light, said he was concerned that the council would sign another contract with Jarvis despite the firm's problems.
"This company's plight is very worrying," he said.
"This is perhaps reflected in the fact that there have been major problems with a number of sites they have been involved in, both in Kirklees and elsewhere.
"My group remains very concerned at the financial implications and costs to the council if this company should fold and the disruption this may cause to education in Kirklees."
Local government union Unison has also expressed fears.
Clr Geoff Alvy, Cabinet member for children's services, said: "Council officers have had and will continue to have detailed discussions with Jarvis, their bankers and with the Department for Education and Skills and also with other councils that are in a similar position."
The contract is being delayed.