One of the most important benefits of computer use within educational settings has been described as its potential for use in collective activity. However; there is a need to take a closer look at the apparently unproblematic picture of children's actual cooperation around the computer. The purpose of this research was to study positions and positioning in peer activity around the computer in pre-school. Data were collected in three different Swedish municipal pre-school units with children from three to six years of age. In this paper three positions, described as "owner", "participant'"and "spectator", are identified and discussed. The positions are static as they constitute a specific space for acting, including rights, duties and obligations. They are also dynamic as, in relation to previous experiences, they appear to imply different opportunities to use the afforded space for acting. The play around the computer implies that positions and positioning are continuously defined and transformed in relation to each other. (Contains 1 note.)