SSRIs alone can double a person's risk of upper GI bleeding, but the risk rises to six-fold if NSAIDs are also taken.
The findings come from a meta-analysis of four studies involving 153,000 patients.
GPs should take a detailed GI history from patients before prescribing SSRIs and try to only give them to those at low risk of upper GI bleeding, say the researchers.
Patients taking SSRIs and NSAIDs should be told to stop taking the painkillers as soon as possible, consider treatment with proton pump inhibitors or switch to a different type of painkiller, the researchers added.
Dr Richard Stevens, Oxford GP and chairman of the Primary Care Society for Gastroenterology, said: 'If you can get away without prescribing SSRIs or NSAIDs, perfect. If you're going to do this, co-prescribe some gastroprotection. But also warn the patient to report any bleeding.'Comment below and tell us what you think