  We evaluate in perturbative QCD, up to order $\alpha_s^4$, the mass of the
$B_c$. We use the so-called 1S-mass in order to improve the convergence of the
perturbative series. Our result is $E(B_c)_{pert} = 6326^{+29}_{-9}$ MeV.
Non-perturbative effects are discussed. A comparison with potential models
seems to be consistent with non-perturbative contributions of the order $ -
(40\div 100)$ MeV.
