Kennet and North Wiltshire Primary Care Trust along with the West Wiltshire Trust made the announcement on Thursday - blaming a savings target of £20m.
The trusts say they want to keep redundancies to a minimum and will redeploy staff where possible.
The two trusts recently announced changes which will see seven community hospitals across the county close.
Bradford-on-Avon, Devizes, Melksham, Savernake, Trowbridge, Warminster and Westbury hospitals face the axe.
The trusts want to replace them with enhanced GP surgeries or 24-hour community teams.
West Wiltshire PCT is currently £7.5m in debt, and Kennet & North Wiltshire is more than £8.2m in the red.
"We will endeavour to let those who may be affected know as quickly as we can."
Carol Clarke, chief executive of the two trusts, said: "As part of our financial recovery plan it will be necessary for the PCTs to make savings by reducing the number of management, administration and support posts, and associated overheads.
"The planned reduction in posts will make a necessary and important contribution to our financial recovery.
"I appreciate that this is a difficult time for everyone in our organizations, and uncertainty about the future only makes it harder. "We will endeavour to let those who may be affected know as quickly as we can."
Staff at the trusts have been informed of the changes and affected employees will be contacted by managers during May.
On Wednesday, Health Secretary Patricia Hewitt was heckled for the second time in three days by health workers.
Ms Hewitt was jeered and slow hand-clapped by nurses at a conference in Bournemouth as she tried to address their fears about NHS deficits.
Hospital trusts across the UK have announced more than 7,000 job cuts in recent weeks because of budget deficits
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