We report on a scanning tunneling spectroscopy investigation at low temperature on oxidized surfaces of highly resistive icosahedral AlPdMn, AlCuFe and AlPdRe phases. The tunneling conductance is found to vary significantly as a function of the scanning tunneling microscope tip location on the surface. A common feature of our quasicrystalline samples is the presence of a zero bias dip, with square root voltage dependence from 5?mV to 300?mV. This is indicative that the one electron density of states has a square root singularity at the Fermi level. More generally, we discuss how tunneling spectroscopy can be used to determine the electronic density of states and its limitation for our quasicrystalline alloys.