A total of 58 jobs in Leeds and Nottingham are under threat in a consultation that began on 6 July 2010.
According to group operations director Catherine Hearn, the redundancies are being made because of changes in the company's contract base.
She said: "Both the sites are affected by the redundancies. We are in consultation with employees to try and minimise the losses as much as possible."
The consultation will come to a close in August. However, Unite regional officer Kathy Brooks said that the union would not accept knee-jerk redundancies.
In March this year, Polestar Applied Solutions won the National Magazine Company direct mail print contract.
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