An ESR study of centres in x-irradiated ammonium perchlorate single crystals is carried out that is aimed at resolving the controversy that has recently arisen over the possible occurrence of low-temperature phase transitions in the compound (room temperature structure: orthorhombic; space group Pnma). The ESR spectra are recorded as a function of the orientation of the magnetic field H in the three orthogonal crystallographic planes at 300 K, 77 K, and 4.2 K, and also as a function of temperature for H parallel to the principal z-component of the hyperfine coupling tensor. The analysis of the spectra shows that while the -tensor remained axial over the entire temperature range 2.0052(3), 2.0055(3), 2.0057(3) and 2.0090(3), 2.0096(3), 2.0105(3) at 300 K, 77 K, and 4.2 K respectively), , which is rhombic at room temperature , , and at 300 K) becomes more axial as the temperature is lowered , , and at 77 K, and , , and at 4.2 K). No changes in the spectra attributable to any phase transition were observed, and we conclude that does not undergo any phase transition below room temperature. Furthermore, it is found that during radiative decomposition the mirror-related Cl - O bonds, even though weaker than the other Cl - O bonds, do not break, thus confirming our earlier conclusion that mirror symmetry is preserved during radiation damage.