  We analysed the ground state energy of some dimerized spin-1/2 transverse XX
and Heisenberg chains with Dzyaloshinskii-Moriya (DM) interaction to study the
influence of the latter interaction on the spin-Peierls instability. We found
that DM interaction may act either in favour of the dimerization or against it.
The actual result depends on the dependence of DM interaction on the distortion
amplitude in comparison with such dependence for the isotropic exchange
interaction.
