  Contents: So far, red giant oscillations have been studied from radial
velocity and/or light curve variations, which reveal frequencies of the
oscillation modes. To characterise radial and non-radial oscillations, line
profile variations are a valuable diagnostic. Here we present for the first
time a line profile analysis of pulsating red giants, taking into account the
small line profile variations and the predicted short damping and re-excitation
times. We do so by modelling the time variations in the cross correlation
profiles in terms of oscillation theory.
  Aims: The performance of existing diagnostics for mode identification is
investigated for known oscillating giants which have very small line profile
variations. We modify these diagnostics, perform simulations, and characterise
the radial and non-radial modes detected in the cross correlation profiles.
  Methods: Moments and line bisectors are computed and analysed for four
giants. The robustness of the discriminant of the moments against small
oscillations with finite lifetimes is investigated. In addition, line profiles
are simulated with short damping and re-excitation times and their line shapes
are compared with the observations.
  Results: For three stars, we find evidence for the presence of non-radial
pulsation modes, while for $\xi$ Hydrae perhaps only radial modes are present.
Furthermore the line bisectors are not able to distinguish between different
pulsation modes and are an insufficient diagnostic to discriminate small line
profile variations due to oscillations from exoplanet motion.
