OBJECTIVES: To study attitudes in the Danish population towards treatment of severely handicapped and extremely preterm infants and to define areas of consensus and controversy. DESIGN: Mail-delivered questionnaire. SETTING: Denmark. Survey sample--A random sample of 1080 persons aged from 18 to 45 years. RESULTS: The overall response rate was 68%. There was strong consensus (more than 75% agreement) that life-prolonging treatment should be provided for an infant born after 24 weeks' gestation with respiratory distress and, for an infant with myelomeningocele, when the parents were in favour of treatment. Further, there was almost uniform agreement that not all infants should be treated no matter how serious the condition. Major controversies concerned the severity of a condition needed to justify omission of life-prolonging treatment, the role of parental attitude and the options in non-treatment cases. Forty-six per cent thought it ought to be legal to kill the infant in at least some of these cases. CONCLUSION: Although the study revealed wide divergences of opinion with regard to questions about limits of treatment and about end-of-life decisions it also showed that there was general acceptance both that life-prolonging treatment ought to be provided even in relatively severe cases if this was in accordance with parental wishes, and that life should not be saved at all costs