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We consider the problem of maximizing the lifetime of a given multicast connection in a wireless network of energy-constrained (e.g., battery-operated) nodes, by choosing ideal transmission power levels for the nodes relaying the connection. We distinguish between two basic operating modes: In a static power assignment, the power levels of the nodes are set at the beginning and remain unchanged until the nodes are depleted of energy. In a dynamic power schedule, the powers can be adjusted during operation. We show that while lifetime-maximizing static power assignments can be found in polynomial time, for dynamic schedules the problem becomes NP-hard. We introduce two approximation heuristics for the dynamic case, and experimentally verify that the lifetime of a dynamically adjusted multicast connection can be made several times longer than what can be achieved by the best possible static assignment.