This thesis elaborates an Actor Network Theory account of the representations through which 'xenotransplantation' (a key facet of the 'new medical biologies') is narrated and extended. In particular, I address the performance (and distribution) of hope across and between xenotransplantation's key network participants. As both a means and a perimeter of network organisation, the temporal dimensions of ordering carry implications for the formation and implementation of Science Studies theory too. ANT, for example, has evolved in relation to a panoply of mainly spatial metaphors (spaces, topologies, differences and similarities etc.). This thesis, by contrast, has sought to respond to the temporal terms of reference which populate representations of xenotransplantation. Amongst other things, competing hopes, desires, right and wrong times, continuities and discontinuities all serve as the principal discursive means through which network management is exercised. My suggestion is that representations of time, as well as the timing of representations, are vital to understanding the production of networks. Also, such terms map onto the many other sense making boundaries which are evoked and challenged through the transpecies exchange of tissues and genes: self and other, human and nonhuman, science and culture, expert and public.