  The real $R_s(T)$ and imaginary $X_s(T)$ parts of the surface impedance
$Z_s(T)=R_s(T)+iX_s(T)$ in polycrystalline MgB$_2$ samples of different density
with the critical temperature $T_c\approx 38$ K are measured at the frequency
of 9.4 GHz and in the temperature range $5\le T<200$ K. The normal skin-effect
condition $R_s(T)=X_s(T)$ at $T\ge T_c$ holds only for the samples of the
highest density with roughness sizes not more than 0.1 $\mu$m. For such samples
extrapolation $T\to 0$ of the linear at $T<T_c/2$ temperature dependences
$\lambda_L(T)=X_s(T)/\omega\mu_0$ and $R_s(T)$ results in values of the London
penetration depth $\lambda_L(0)\approx 600$ \AA and residual surface resistance
$R_{res}\approx 0.8$ m$\Omega$. In the entire temperature range the dependences
$R_s(T)$ and $X_s(T)$ are well described by the modified two-fluid model.
