  A considerable fraction of Galactic supernova remnants (SNRs) characterize
flat spectral indices ($\alpha<0.5$). There are several explanations of the
flat radio spectra of SNRs in the present literature. The most of models
involve a significant contribution of the second-order Fermi mechanism but some
of them also discuss high compressions (>4), contribution of secondary
electrons left over from the decay of charged pions, as well as the possibility
of thermal contamination. In the case of expansion in high density environment,
intrinsic thermal bremsstrahlung could theoretically shape the radio spectrum
of an SNR and also account for observable curved -- "concave up" radio spectra
of some Galactic SNRs. This model could also shed a light on the question of
flat spectral indices determined in some Galactic SNRs. On the other hand,
present knowledge of the radio continuum spectra (integrated flux densities at
different frequencies) of SNRs prevent definite conclusions about the
significance of proposed models so the question on flat spectral indices still
remains open. New observations, especially at high radio continuum frequencies,
are expected to solve these questions in the near future. Finally, as there is
a significant connection between the majority of Galactic SNRs with flat
integrated radio spectrum and their detection in $\gamma$-rays as well as
detection of radiative recombination continua in their X-ray spectra, the
analysis of high energy properties of these SNRs is very important.
