The bright persistent X-ray source and type I X-ray burster 1E1724-3045 located in the globular cluster Terzan 2 was observed by ASCA for about 10 ksec on September 24-25th, 1995 while it was in its hard state, with a luminosity of \~6x10^36 erg/s in the 0.5-10 keV band (d=7.7 kpc). The ASCA spectrum is hard, and reveals the presence of a soft component below 2-3 keV. When combined with non simultaneous RXTE/HEXTE data, we show that the ASCA spectrum can be adequately fitted by a Comptonization model for which the electron temperature is ~30 keV, the optical depth is ~3 for a spherical scattering cloud. The soft component carries off about 13%, and 35% of the 0.1-200 keV luminosity for a blackbody and disk blackbody fit respectively. It is more likely to arise from the accretion disk, whereas the hard Comptonized component is generated in a hot boundary layer interior to the disk. The column density measured towards the source (NH=10^22 cm^-2) is consistent with the value expected from the optical reddening of the cluster. No emission lines were detected, and an upper limit of 30 eV for the equivalent width of a 6.4 keV line (sigma=0.1 keV) has been derived.