But this "monitoring and frequent check-ups of symptoms" does not reduce their heart risk, the researchers said. Instead, the "persistent and exaggerated attention to symptoms" risks "placing strain on bodily systems and, in turn, increasing the risk of cardiovascular diseases".
They examined participants' levels of health anxiety through questionnaires then tracked them over 12 years. Of those who had scored in the top 10 per cent for health anxiety, 6.1 per cent either had a heart attack or developed angina - more than twice the rate of those who did not have health anxiety.
Some doctors believe that stressed people are more at risk because they are more likely to drink, smoke or eat badly. Others may not exercise, because they are worried about putting their bodies in harm's way.
But the Norwegian scientists found that even when they adjusted the figures to take such risk factors into account, those with health anxiety at the start of the study were 73 per cent more likely to develop heart disease, showing that stress is an "independent risk factor" for heart disease.
They believe this is caused by high activation of the parts of the body which control stress hormones such as cortisol and adrenaline. The researchers found that men were more likely to be affected, with anxious men at a 78 per cent higher risk of heart disease. For anxious women it was 58 per cent.
Dr Gavin Sandercock, of the University of Essex, said: "Stress definitely plays a role in causing heart disease. Some research suggests that three-quarters of the risk is biological and a quarter is psychological - so it is not the biggest factor, but it is a factor.
"If you are stressed your blood pressure goes up, your heart rate goes up and long-term it is has an impact on your health.
"It is a vicious cycle, you get anxious about your health, so you smoke or you do not exercise, and then you get anxious about the impact that has on your health, and it continues."
A Swiss study in 2012 suggested that people with a more positive outlook on life were more likely to live longer.