This article reports the results of a survey, by mailed questionnaire, of the attitudes among a sample of the Danish population towards abortion for social and genetic reasons. Of 1080 questionnaires sent to a random sample of persons between 18 and 45 years, 731 (68%) were completed and returned. A great majority of the respondents were liberal towards early abortion both for social reasons and in case of minor disease. In contrast, there was controversy about late abortions for social reasons and in the case of Down syndrome. Further there was strong reluctance to accept late abortion in case of minor disease. An analysis of the response patterns showed that most of the respondents had gradualist views on abortion, i.e. they would allow all early abortions, but only abortions for some reasons later in pregnancy. It was also found that the number who would find an early abortion acceptable in general was much higher than the number who would accept it in their own case. These findings suggest that a great part of the resistance towards abortion does not rest on a concern for the rights and interests for the fetus. Instead it may be explained on a view according to which fetal life is ascribed intrinsic moral value.