  We introduce the notion of finite BRST-antiBRST transformations for
constrained dynamical systems in the generalized Hamiltonian formalism, both
global and field-dependent, with a doublet $\lambda_{a}$, $a=1,2$, of
anticommuting Grassmann parameters and find explicit Jacobians corresponding to
these changes of variables in the path integral. It turns out that the finite
transformations are quadratic in their parameters. Exactly as in the case of
finite field-dependent BRST-antiBRST transformations for the Yang--Mills vacuum
functional in the Lagrangian formalism examined in our previous paper
[arXiv:1405.0790[hep-th]], special field-dependent BRST-antiBRST
transformations with functionally-dependent parameters $\lambda_{a}=\int
dt\(s_{a}\Lambda) $, generated by a finite even-valued function $\Lambda(t)$
and by the anticommuting generators $s_{a}$ of BRST-antiBRST transformations,
amount to a precise change of the gauge-fixing function for arbitrary
constrained dynamical systems. This proves the independence of the vacuum
functional under such transformations. We derive a new form of the Ward
identities, depending on the parameters $\lambda_{a}$, and study the problem of
gauge-dependence. We present the form of transformation parameters which
generates a change of the gauge in the Hamiltonian path integral, evaluate it
explicitly for connecting two arbitrary $R_{\xi}$-like gauges in the
Yang--Mills theory and establish, after integration over momenta, a coincidence
with the Lagrangian path integral [arXiv:1405.0790[hep-th]], which justifies
the unitarity of the $S$-matrix in the Lagrangian approach.
