The article critiques the theoretical basis for researching global cities as structures, networks, and actor-networks. First, Sassen's and Taylor's concepts for global urban command are closely examined to reveal, amongst other things, their inherent contradiction. This revelation is of fundamental importance because current research is proceeding apace on the assumption of their compatibility. Second, we move beyond a critique of structures and networks to expose a problem with re-conceptualizing cities as actor-networks. We explain how actor-network theory runs aground on a ‘plasma’ and consequently suggest a route out of that theoretical impasse by arguing for a re-conceptualization of cities modelled on the work of Badiou. Finally, we demonstrate how such a conceptual shift provides the theoretical basis for a new type of urban analysis that examines how cities strive to prohibit and dissimulate their unbinding and destabilization as networks. Thus, the article advances a new model for global-urban studies about how cities as networks are fragile, ongoing achievements, not only because — as actor-network theory has taught us — they hold together only because they are held together, but because — as Badiou shows us — they are blind to what they cannot take into account: multiplicity and event as products of subtraction.