Electromagnetic creeping waves on a 3-dimensional surface with an anisotropic impedance boundary condition are considered. The influence of the impedance is examined. The standard asymptotic formula for the creeping waves contains the factor 1/(τ - q²) where τ is the attenuation parameter and q is the Fock parameter which depends on the impedance matrix. Analysis of the equation for the attenuation parameter which describes its dependence on q shows that there exist such critical values of q when the factor 1/(τ - q²) diverges and the usual asymptotic formula gives infinite result. The equation for the critical values of the parameter q is derived and the 4 first critical values are found numerically. The new local asymptotics valid in domain of the size κ^-2/9 (where κ is the wave number) is derived in the supposition that the divergence takes place on a curve crossed by creeping waves. This new asymptotic decomposition is carried out by powers of the small parameter κ^-1/9. The effect of creeping wave passing through the line where the usual asymptotics diverges is examined.