  We present a general theory of quasiprobability distributions on phase spaces
of quantum systems whose dynamical symmetry groups are (finite-dimensional) Lie
groups. The family of distributions on a phase space is postulated to satisfy
the Stratonovich-Weyl correspondence with a generalized traciality condition.
The corresponding family of the Stratonovich-Weyl kernels is constructed
explicitly. In the presented theory we use the concept of the generalized
coherent states, that brings physical insight into the mathematical formalism.
