They include unusual tiredness, disturbed sleep patterns, shortness of breath and indigestion.
Some happen up to a month ahead of a heart attack, which could give doctors time to prevent it if they were alerted.
But far fewer women than men experience the 'classic' symptom of chest pain before an attack.
Professor Jean McSweeney, who carried out the study, said: 'Lack of significant chest pain may be a major reason why women have more unrecognised heart attacks than men and are mistakenly diagnosed and discharged from emergency departments.'
Another factor is that many women are still unaware of the toll taken on their sex by heart disease, which claims five times as many lives in the UK as lung and breast cancers combined.
In the latest study, U.S. researchers questioned more than 500 women in their sixties who had suffered heart attacks.
Almost all reported feeling new or different symptoms some weeks before their heart attack. Seven out of ten had unusual fatigue and almost half suffered disturbed sleep and shortness of breath.
Around four out of ten had indigestion while a third reported feelings of anxiety.
Only one in three reported chest discomfort before the attack, and said it had felt like aching, tightness and pressure rather than pain.
Four out of ten women did not even feel chest pain during the heart attack itself, and those who did said the pain was in the back and high chest, rather than the centre.
The results are reported in the medical journal Circulation.
Professor McSweeney, from the College of Nursing at the University of Arkansas for Medical Sciences in Little Rock, said previous research by her team had found women often brushed aside possible symptoms or were misdiagnosed if they did seek help.
She said: 'Women need to be educated that the appearance of new symptoms may be associated with heart disease and that they need to seek medical care to determine the cause of the symptoms, especially if they have known risk factors such as a family history of heart disease.'
Dr Duncan Dymond, consultant cardiologist at St Bartholomew's Hospital, London, said last night that statistics show that, as women get older, they run an even greater risk of dying from heart disease than men.
He said: 'Heart disease is a bigger killer for women than breast cancer or cancer of the cervix.
'We can expect to see more and more heart disease in women as the population of the UK ages and the proportion of women in the population increases.'
Dr Dymond, who has just written The Plain English Guide to Heart Disease, said women get a 'raw deal' because of bias in the system and possibly their own unwillingness to see themselves as being at risk of a heart attack.
He said: 'Women often say they had experienced chest tightness after a heart attack is diagnosed but they may have thought it just doesn't happen to women. They also tend to be more stoical then men.
'Both men and women often feel unusually tired in the days running up to a heart attack and this new study shows the importance of not dismissing this.
'It's obviously difficult because many people complain of feeling "tired all the time" but you should take notice if this is coupled with other symptoms such as shortness of breath which you didn't have when you walked upstairs last week.
'I'd much rather people came to me with these symptoms than just ignored them and hoped they would go away - and I suspect most GPs would agree.'
Dr Dymond said doctors wrongly assume that women are less likely to suffer from cardiac symptoms and that treatment is less effective in women than in men.
He added: 'Latest research shows that when women get the correct diagnosis and treatment for heart problems the results are as good as they are in men.'
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