The qualitative explanation of the temperature dependence of the linewidth
of electron-paramagnetic resonance (EPR) in alpha'-NaV2O5 is proposed. Our
simple theory is based on the effectively one-dimensional quantum descripti
on of effective spin-spin interactions. We explain the high-temperature inc
rease of the EPR linewidth with increasing temperature by the influence of
the effective magnetic anisotropy of spin-spin interactions. The low-temper
ature upturn of the temperature dependence of the EPR linewidth is explaine
d by the effect of period doubling of the exchange interaction of the effec
tive quasi-one-dimensional spin subsystems. Our theory does not demand the
controversial presence of the staggered Dzyaloshinskii-Moriya interactions
at high temperatures.