Observations of two unclassified Low Mass X–ray Binaries , X1543–624 and X1556–605 , are presented . In the 2–10 keV band the first of the two sources is a factor of two stronger than the other . Both sources do not show X–ray bursts , dips or eclipses in their X–ray light curves . We find that both spectra are described by a two–component model consisting of emission from a cool accretion disk plus a Comptonized blackbody with kT _ { bb } \sim 1.5 keV in a low opacity plasma . The spectrum of X1543–624 hardens from the first to the second observation , when the source slowly moves from right to left in the colour–colour diagram . The spectrum of X1556–605 can also be described by a model consisting of a blackbody plus an unsaturated Comptonization with electron energy kT _ { e } \sim 4 keV . In the first observation , X1543–624 shows evidence of a Fe K emission line at 6.4 keV . Moreover , in both observations , the source spectrum exhibits an emission feature around 0.7 keV , which is interpreted as due to the superposition of the K edge absorption features of O and Ne elements with uncommon relative abundances with respect to the solar one ( O/O _ { \odot } \sim 0.3 , Ne/Ne _ { \odot } \sim 2.5 ) . In the spectrum of X1556–605 no emission lines are observed . We discuss these results and their implications for the source classification and the accretion geometry of the compact object .