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The leaderless and leader-following finite-time consensus problems for multi-agent systems (MASs) described by first-order linear hyperbolic partial differential equa-tions (PDEs) are studied.The Lyapunov theorem and the unique solvability result for the first-order linear hyperbolic PDE are used to obtain some sufficient conditions for ensuring the finite-time consensus of the leaderless and leader-following MASs driven by first-order linear hyperbolic PDEs.Finally,two numerical examples are provided to verify the effectiveness of the proposed methods.