  In this paper we consider the Maslov S^{1}bundles of a symplectic manifold
(M,\omega), which refer to both the determinant bundle (denoted by \Gamma_{J})
of the unitary frame bundle and the bundle
\Gamma_{J}^{2}=\Gamma_{J}\big/\{\pm1\}. The sympletic action of a compact Lie
group G on M can be lifted to group actions on the principal S^{1} bundles
\Gamma_{J} and \Gamma_{J}^{2}. In this work we study the interplay between the
geometry of the Maslov S^{1} bundles and the dynamics of the group action on M.
We show that when M is a homogeneous G-space and the first real Chern class
c_{\Gamma} is nonvanishing, \Gamma_{J} and \Gamma_{J}^{2} are also homogeneous
G-spaces. We also show that when [\omega]=r\cdot c_{\Gamma} for some real
number r, then the G action is Hamiltonian and the Hamiltonians assume
particular forms. In the end, we study a function called the \beta-Maslov data
of a symplectic S^{1} action with respect to a connection 1-form \beta on
\Gamma_{J}^{2}, which serves as the nonintegrable version of the notion of
Maslov indices when \Gamma_{J}^{2} is not a trivial bundle.
