  We give bijective proofs of orthosymplectic analogues of the Cauchy identity
and dual Cauchy identity for orthosymplectic Schur functions. To do so, we
present two insertion algorithms; these are orthosymplectic versions of
Berele's symplectic insertion algorithms, which were used by Sundaram to give
bijective proofs of Cauchy identities for symplectic Schur functions.
