  We analyze generalized Gaussian cat states obtained by superposing arbitrary
Gaussian states, e.g., a coherent state and a squeezed state. The Wigner
functions of such states exhibit the typical pair of Gaussian hills plus an
interference term which presents a novel structure, as compared with the
standard superposition of coherent states (degenerate case). We prove that, in
any dimensions, the structure of the interference term is characterized by a
particular quadratic form; in one degree of freedom the phase is hyperbolic.
This phase-space structure survives the action of a thermal reservoir. We also
discuss certain superpositions of {\em mixed} Gaussian states generated by
conditional Gaussian operations or Kerr-type dynamics on thermal states.
