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The stability of the Schwarzschild metric against small perturbations is discussed in Brans-Dicke theory. The perturbations superposed on the Schwarzschild background state are composed of odd, even parities of gravitational perturbations, and scalar perturbations. By the familiar procedure of analyzing the black-hole stability, we have found that all nonstatic perturbations allow only the real values of frequency k, which means that this system is classically stable. However, for k=O, an odd perturbation with L > 1 and even and pure scalar perturbations with all L 2 0 are classically unstable because all of these cases allow the exponentially growing modes.

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