  Equivalence between algebraic structures generated by parastatisticstriple
relations of Green (1953) and Greenberg -- Messiah (1965), and certain
orthosymplectic $\mathbb{Z}_2\times \mathbb{Z}_2$-graded Lie superalgebras is
found explicitly. Moreover, it is shown that such superalgebras give more
complex para-Fermi and para-Bose systems then ones of Green -- Greenberg --
Messiah.
