Another two weeks of strikes have been announced for staff at Bradford Royal Infirmary and St Luke's.
Hundreds of non-medical staff, including porters, domestics, security and catering employees, went on strike on Thursday.
The row is due to plans from Bradford Teaching Hospitals Trust to outsource jobs to the private sector in order to cut costs.
Under the strategy, roles would be transferred to a wholly-owned subsidiary (WOS) company set up by the Trust.
Unison members believe pay and pensions will suffer as a result of the changes.
General secretary for Unison Dave Prentice said: "Staff are taking this action to ensure the NHS keeps its highly motivated and committed workforce together, working for the people of Bradford, not for the directors of a private company.
"It doesn't reflect well on the trust that staff who are proud to be part of the NHS have to take to the streets to convince the trust that patients and staff come before profits."
The strike, which is from 6am on Thursday, August 1, to 6am on Thursday, August 15, follows a week of industrial action in July. Hospitals affected include Bradford Royal Infirmary and St Luke's Hospital.
A statement on the Bradford Teaching Hospitals website said: "Arrangements have been made to ensure that patient safety and levels of care are not compromised by this action and all essential services, such as emergency and urgent surgery, will continue as normal.
"Patients should attend their routine clinics and appointment as normal unless notified otherwise.
"The creation of a WOS company is not privatisation. The Trust Board has explicitly decided against outsourcing our Estates, Facilities and Clinical Engineering services because we believe we wouldn’t be able to retain the same level of influence over the quality of the service, or guarantee protection for staff terms and conditions in the long-term.
"Furthermore, we want these services to continue to work to the core Trust values and be part of the NHS family."