Context: 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 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.
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