  We consider the spin-1/2 isotropic $XY$ chain in an external magnetic field
directed along $z$ axis with periodically varying $g$-factors. To reveal the
effects of regularly alternating $g$-factors, we calculate various static and
dynamic equilibrium quantities in the ground state and at finite temperatures.
We demonstrate that because of the regularly alternating $g$-factors the
saturation field may disappear and the field dependence of the susceptibility
in the ground state has additional logarithmic singularity at zero field.
Moreover, the zero-field susceptibility has a logarithmic singularity as $T\to
0$. Furthermore, the dynamic structure factors exhibit much more structure in
the "wave vector -- frequency" plane that can be traced out to modifications of
the two-fermion excitation continua which exclusively determine
$S_{zz}(\kappa,\omega)$ and dominate the properties of $S_{xx}(\kappa,\omega)$.
We discuss what changes can be observed in dynamic experiments on the
corresponding substances.
