The straight line and the circle, respectively, are the traditional geometrical representations of time. According to the linear conception time is progressive. Strictly speaking, nothing will stay as it was, everything will change. Even if a phenomenon appears to be stable, say, the whiteness of an object, it is still not seen to be identical with’ same’ phenomenon one moment ago — since that phenomenon does not really exist as opposed to the phenomenon we are contemplating ‘now’, and which does exist. According to the circular conception of time nothing is really new. Any event is a repetition of previous events, and will be repeated indefinitely in the future. These two geometrical images of time have been dominant within the philosophy of nature and other strands of systematic thinking from the antiquity and up to this century. However, during the last decades a number of intellectuals have suggested a new kind of time models. According to these models time is viewed as a branching system — a tree-structure. Since branching time models are very important in the modern analysis of temporality, it is worth trying to understand this new image of time in relation to the history of ideas.