  The clear detection with CoRoT and KEPLER of radial and non-radial solar-like
oscillations in many red giants paves the way to seismic inferences on the
structure of such stars. We present an overview of the properties of the
adiabatic frequencies and frequency separations of radial and non-radial
oscillation modes, highlighting how their detection allows a deeper insight
into the properties of the internal structure of red giants. In our study we
consider models of red giants in different evolutionary stages, as well as of
different masses and chemical composition. We describe how the large and small
separations computed with radial modes and with non-radial modes mostly trapped
in the envelope depend on the stellar global parameters and evolutionary state,
and we compare our theoretical predictions and first KEPLER data.Finally, we
find that the properties of dipole modes constitute a promising seismic
diagnostic of the evolutionary state of red-giant stars.
