  We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend
a new approach of the construction of the spinor and metaplectic $\hat{\cal
R}$-operators with orthogonal and symplectic symmetries to the supersymmetric
case of orthosymplectic symmetry. In this approach the orthosymplectic
$\hat{\cal R}$-operator is given by the ratio of two operator valued Euler
Gamma-functions. We illustrate this approach by calculating such $\hat{\cal R}$
operators in explicit form for special cases of the $osp(n|2m)$ algebra, in
particular for a few low-rank cases. We also propose a novel, simpler and more
elegant, derivation of the Shankar-Witten type formula for the $osp$ invariant
$\hat{\cal R}$-operator and demonstrate the equivalence of the previous
approach to the new one in the general case of the $\hat{\cal R}$-operator
invariant under the action of the $osp(n|2m)$ algebra.
