Nine out of 10 had levels indicative of "significant exposure", says a Scandinavian study in the US Journal of Pediatrics.
It provides the first direct evidence linking nicotine and cot deaths, adding weight to earlier research indicating that parents who smoke put their babies at risk.
The study is the first to measure directly levels of nicotine in the children's bodies to see whether death coincides with heavy parental smoking. Previous studies linking smoking and cot death have relied on what parents said about their smoking habits. That was not considered scientifically reliable.
The team, led by Joseph Milerad, neonatologist at the Department of Women and Child Health in the Karolinska Institute, Stockholm, took samples of pericardial fluid, the fluid present in the sac surrounding the heart, from every child under seven who had died suddenly in the greater Oslo region between 1990 and 1993. The 45 consecutive victims included 24 dying from sudden infant death syndrome, or SIDS. The rest died in accidents or from infection. The pericardial fluid was tested for the nicotine by- product cotinine, which, because of the way the body metabolises the nicotine, indicates the level of exposure from four to eight hours before death.
The research team could not compare nicotine levels in the cot death babies with normal healthy babies, as they would have liked, because blood samples from the cot death victims were not available, and taking pericardial fluid from around the heart could not be performed on healthy babies. They were therefore left with a control group of children who had died in accidents or of infections.
Among the children who died of infections, two-thirds showed evidence of nicotine exposure but none had the high levels found in a quarter of the cot death victims.
Dr Milerad said current advice not to smoke near babies and children was not strong enough. He said the advice was based on averting diseases such as asthma, but the study suggested that nicotine posed a more direct risk. Studies of rats and unborn babies have indicated that exposure to nicotine depresses the body's response to a fall in oxygen and delays arousal from sleep.
He said: "If you ask mothers whether they smoke near their babies, you get the answer that it's not so much - but we have shown how strong the link is between smoking and cot death."
The study concludes that "SIDS is in almost all cases preceded by a significant exposure to nicotine, (and) acute heavy exposure may play a role in the mechanisms of SIDS".
A spokeswoman from the Foundation for the Study of Infant Deaths said: "This study confirms the findings of FSID-funded research and other studies worldwide, clearly showing that babies exposed to tobacco smoke are at increased risk of cot death. It supports advice that mothers should cut out smoking during pregnancy - fathers too. Parents should create a smoke-free zone by not smoking in the same room as their baby and by avoiding smoky atmospheres."