In this study we test the possibility that the asymmetry in the profiles of the H-alpha and Ca II K lines in red giant stars is due to the presence of an active chromosphere rather than to mass loss. To this end, we compare line profiles computed using relevant model chromospheres to profiles of the H-alpha and Ca II K lines observed in five red giant stars of the globular cluster NGC 2808. The spectra were taken with FLAMES during Science Verification, using the UVES mode at high resolution (R=43,000) for the H-alpha line, and GIRAFFE in MEDUSA mode (R=20,000) for the Ca II K line. We find that the observed profiles are better described if a negative (outward) velocity field is included in the model chromospheres. This leads to mass loss rates of a few 10**(-9) solar masses per year, very close to the requirements of the stellar evolution theory.