  The question of the integrability of the mixmaster model of the Universe,
presented as a dynamical system with finite degrees of freedom, is investigated
in present paper. As far as the model belongs to the class of pseudo-Euclidean
generalized Toda chains, the method of getting Kovalevskaya exponents developed
for chains of Euclidean type, is used. The generalized formula of Adler and van
Moerbeke for systems of an indefinite metric is obtained. There was shown that
although by the formula we got integer values of Kovalevskaya exponents there
were multivalued solutions, branched at particular points on a plain of complex
time t. This class of solutions differs from known ones. Apparently, the system
does not possess additional algebraic and one-valued first integrals because of
complex and transcendental values of the exponents. In addition, a
ten-dimensional mixmaster model was studied. There were not integer exponents
for this case.
