Ionization or ionic dissociation of perchloric acid in the clusters HClO4-(H2O)(n) (n = 1-3) and HClO4-NH3-(H2O)(n) (n = 0, 1) is investigated by density functional theory and ab initio molecular orbital theory. The equilibrium structures, binding energies, and dipole moments of the clusters are calculated using the hybrid density functional (B3LYP) method with the 6-31+G* and 6-311++G** basis sets and the second-order Moller-Plesset approximation method with the 6-311++G** basis set. Harmonic vibrational frequencies are obtained from the B3LYP/6-311++G** calculations. Perchloric acid is found to require a minimum of three water molecules for ionization to occur and at least one water molecule to protonate ammonia. The corresponding clusters with fewer water molecules are found to be strongly hydrogen-bonded. The acid strength and the related properties of perchloric acid are discussed and compared to those of sulfuric acid in the context of clusters with ammonia and water.