As part of the Better Together campaign, Borders MP Michael Moore and Julie Pörksen have met to discuss healthcare with Berwick councillors.
Patients currently travel across the border to access GP, emergency and hospital care.
Michael Matheson, the Scottish Government’s public health minister insisted last month that existing cross-border agreements would not be affected if Scotland votes for independence.
However, the Lib Dems say the agreements may change.
Mr Moore said: “Should Scotland vote to become independent this September it is far from certain that patients across the Borders and in Berwick would continue to receive cross-border care.
“The close bond between healthcare providers in England and Scotland is hugely beneficial to people living close to the border and we cannot afford to see this relationship end.”
Julie Pörksen, who will contest Berwick’s Westminster seat for the Lib Dems at the next general election, added: In the debate for independence we must adopt a practical approach which addresses patients needs wherever they live and keep health care as a priority.”
“Concerns have been raised by residents in villages close to the border such as Norham that they may not be able to have the same access to their Scottish GPs should Scotland become independent.
“Many people in Berwick and surrounding areas have also told me that they really want to be able to use the Borders General Hospital and don’t want to see any restrictions that might come about with independence.”