The present catalogue contains 182 low resolution optical spectra, 145 medium resolution (R~1100) near-IR spectra, and 112 merged optical+near-IR spectra that range from about 510 to 2450 nm. The observed stars are luminous cool objects: the sample includes red giants, red supergiants, oxygen rich and carbon rich long period variables (asymptotic giant branch stars), as well as a few Galactic Bulge and LMC/SMC stars. The optical data were acquired on the so-called 74 inch Telescope at Mount Stromlo Observatory. The near-IR data were acquired with the Cryogenic Array Spectrometer and Imager CASPIR on the 2.3 meter Australian National University Telescope at Siding Spring Observatory. Optical and near-IR data for variable objects have been merged only when both were taken less than 15 days apart; but both spectral ranges are also provided separately. The spectra are corrected for telluric absorption. However, in regions where the transmission of the Earth atmosphere is close to zero the fluxes recovered remain highly uncertain. The flux calibration is based on a series of reference stars, for which a theoretical intrinsic energy distribution was assumed. An absolute flux calibration (to about 10% accuracy) was only achieved in exceptional cases; in the other cases, the absolute fluxes can be off their real values by an order of magnitude due to slit losses (for the programme star and/or the reference star) and to non-photometric wheather. Uncertainties in the relative values of fluxes along each spectrum are described in the paper.