The authorities say the rising cost of children's social care is heaping pressure on their finances.
Warrington Council said it was "increasingly difficult" to achieve a balanced budget, with children's services costs expected to be about 29% over budget.
Sarah Hall, cabinet member for children's services, said: "There are not enough placements [for children] of the right kind, in the right places, and affordability of suitable placements has increased significantly." Neighbouring Cheshire West and Chester Council said its children's services are set to have a £12.4m overspend.
It added there has also been more high-cost residential placements, with 15 placements currently costing more than £10,000 per week.
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