  We study the phase dynamics and IV--characteristics of DC--SQUIDs consisting
of Josephson junctions with topologically nontrivial barriers, which cause the
appearance of Majorana bound state. Its comparative analysis with the trivial
case is performed. The influence of external electromagnetic radiation is
considered and the analysis of the amplitude dependence of the Shapiro step
widths is performed. We have shown that in nontrivial case the width of even
harmonic of Shapiro step is larger than width of odd harmonic. In the presence
of external dc magnetic field a beating state is realized in the DC--SQUID,
which leads to a resonance branch in the IV--curve. We show that in the
presence of resonance branch the maximum width of Shapiro step and periods of
its amplitude dependence are decreased in comparison of situation without
resonance in both trivial and nontrivial cases. We demonstrate that in the
presence of the resonance branch the chaotic behavior of IV--curve is reduced.
