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We evaluate the speed of convergence in the Bohr-Jessen type of limit theorem on the value-distribution of Dedekind zeta-functions of number fields. When K is a Galois number field, the Euler product of the corresponding Dedekind zeta-function (K(s) is convex, hence the evaluation can be done similarly to the case of the Riemann zetafunction. However, when K is non-Galois, some new ideas (based on the Artin-Chebotarev density theorem etc) are necessary, because the corresponding (K(s) is not always convex. §

On the speed of convergence to limit distributions for Dedekind zeta-functions of non-Galois number fields