British troops who have fought in Iraq or Afghanistan suffer far lower rates of post-traumatic stress than Americans do, according to the most rigorous psychiatric study of Britain’s military so far.

While estimated rates of the condition in troops returning to the United States range from 10 to 15 percent, the new study found a rate of just 4 percent among Britons — even though they and the Americans have seen equal amounts of combat in recent years.

When British researchers first reported low rates of post-traumatic stress, in 2006, the Americans were suffering far more casualties in Iraq. But the new study found no increase in mental health problems in British troops from 2003 to 2009, despite an escalating role in active combat in Afghanistan and rising rates of multiple deployments. The findings, being reported in the current issue of The Lancet, are likely to stir debate about why the numbers are so different. In both countries, mental problems still carry a strong stigma among many military people, and both governments have taken extensive measures to prevent and treat combat stress.

“This is truly a landmark study, in its size and rigor, and the findings are surprisingly positive,” said Richard J. McNally, a psychologist at Harvard. “The big mystery is why we find these cross-national differences.”