We demonstrate a sequence of two quantum teleportations of optical coherent states, combining two high-fidelity teleporters for continuous variables. In our experiment, the individual teleportation fidelities are evaluated as F_1 = 0.70 pm 0.02 and F_2 = 0.75 pm 0.02, while the fidelity between the input and the sequentially teleported states is determined as F^{(2)} = 0.57 pm 0.02. This still exceeds the optimal fidelity of one half for classical teleportation of arbitrary coherent states and almost attains the value of the first (unsequential) quantum teleportation experiment with optical coherent states.
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