That's the finding of a study in the Proceedings of the National Academy of Sciences.
Selective serotonin reuptake inhibitors, or SSRIs, are the most common antidepressants and are used by millions of people.
Scientists say the potential interaction between these drugs and some painkillers may be a reason that some people don't respond.
Why this happens no one knows for sure. But, scientists say, doctors need to ask patients about pain killers before they prescribe an antidepressant.