The protest, organised by the GMB union, took place outside a meeting of the Cambridgeshire and Peterborough Clinical Commissioning Group (CPCCG).
The union said outsourcing the multi-million pound contract was a move towards breaking up the NHS.
But the CPCCG said the bidders were a mix of named NHS and private providers.
Steve Sweeney, GMB regional organiser, said the protest near the Masonic Hall in Cambridge was part of its "fight to defend NHS services".
He said: "The NHS should be publicly run, publicly owned and publicly accountable."
Five bidders are in the running:
Clinical lead for the CPCCG's older people's programme Dr Arnold Fertig said: "There is a mix of named NHS and private providers bidding in the procurement process.
"This process is about getting the best possible health services for older people and providing them in joined-up and innovative ways.
"The intention is that older people will experience a much better service than what is currently being offered. We are following a legally agreed procurement process."
A demonstration against outsourcing Cambridgeshire healthcare services for older people has been held as bidders for the contract were announced.