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The decay constants of the low lying S-wave $B_c$ mesons, i.e. $B_c(nS)$ and$B^*_c(nS)$ with $n\leq 3$, are calculated in the nonrelativistic quark model.The running coupling of the strong interaction is taken into account, and theuncertainties due to varying parameters and losing Lorentz covariance areconsidered carefully. As a byproduct, the decay constants of the low lyingS-wave charmonium and bottomium states are given in the appendixes.

The Decay constants of $B_c(nS)$ and $B^*_c(nS)$