  We calculate exactly the density of magnon states of the regularly
alternating spin-1/2 XX chain with Dzyaloshinskii-Moriya interaction. The
obtained results permit us to examine the stability of the chain with respect
to spin-Peierls dimerization. We found that depending on the dependences of
Dzyaloshinskii-Moriya interaction on distortion amplitude it may act either in
favour of the dimerization or against the dimerization.
