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This paper presents a new algorithm for online routing of bandwidth-guaranteed multicasts where routing requests arrive one by one without there being any a priori knowledge of future requests. A multicast routing request consists of a source s, a set of receivers R, and a bandwidth requirement b. This multicast routing problem arises in many contexts. Two applications of interest are routing of point-to-multipoint label-switched paths in multiprotocol label switched (MPLS) networks, and the provision of bandwidth-guaranteed virtual private network (VPN) services under the "hose" service model [18]. Offline multicast routing algorithms cannot be used since they require a priori knowledge of all multicast requests that are to be routed. Instead, online algorithms that handle requests arriving one by one and that satisfy as many potential future demands as possible are needed. The newly developed algorithm is an online algorithm and is based on the idea that a newly routed multicast must follow a route that does not interfere too much with network paths that may be critical to satisfy future demands. We develop a multicast tree selection heuristic that is based on the idea of deferred loading of certain critical links. These critical links are identified by the algorithm as links that, if heavily loaded, would make it impossible to satisfy future demands between certain ingress-egress pairs. The presented algorithm uses link-state information and some auxiliary capacity information for multicast tree selection and is amenable to distributed implementation. Unlike previous algorithms, the proposed algorithm exploits any available knowledge of the network ingress-egress points of potential future demands, even though the demands themselves are unknown, and performs very well.