The aim of this study is to increase our understanding of the attitudes towards the scientific search for extraterrestrial life among high school and university students in Sweden. The most important results of the analysis are that: (a) the great majority of students believe that extraterrestrial life exists; (b) most students regard searching for extraterrestrial life to be quite important or very important; (c) very few students think that we should actively avoid searching for extraterrestrial life; (d) the most common motive for assigning a high priority to search for extraterrestrial life is that it is interesting, the most common motive for assigning a low priority is that such knowledge would not be practically useful, or that the money would be better spent elsewhere; (e) most students do not think they are very well informed regarding the search for extraterrestrial life. A higher percentage of the students who judge themselves to be well informed also believe that extraterrestrial life exists. We have also found some differences between subgroups (men/women, high school students/university students and different fields of study), but the differences are with few exceptions small in comparison with the overall trends, and they mostly differ in degree rather than direction.