****************************************************** PR # 32108 We propose to investigate the X-ray spectral properties of the five X-ray bursters which have shown hard X-ray emission ($\geq$ 150 keV) in SIGMA observations, namely KS1731-260, X1734-308 in Terzan 2, SLX1 732-304 in Terzan 1, A1742-294, and finally GX354-0. These sources are all low-luminosity systems ($L_x \leq 10^{37}$ ergs s$^{ -1}$), and have been poorly studied in X-rays. With ASCA, we will ans wer the following questions {\it 1)} Do these sources define a new class of neutron star systems? {\it 2)} How do their properties com pare with those of the better-studied bursters with power-law tails i n X-rays? and {\it 3)} Can we constrain the origin of hard X-ray emis sion as required for on-going theoretical investigations? ASCA, tha nks to its improved sensitivit ******************************************************