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A detailed study is made on the luminescence of Pb('2+) ions in alkali halide single crystals. The emission spectra of KX:Pb('2+) (X = Cl, Br, I) excited in the A-absortpion band at various temperatures are reported. In addition, the excitation spectra of the A-band emission measured at 4.2 and 78 K are also given. The temperature dependence and the effect of an external magnetic field on the decay time of the A-band emission from KX:Pb('2+) is also investigated. / The results are interpreted in terms of a model that includes the Jahn-Teller effect, the spin-orbit interaction and an additional perturbation caused by the charge compensating cation vacancy (CV, v(,c)('-)). In this model, the Jahn-Teller effect is much smaller than the spin-orbit interaction and the CV is smaller still. The experimental results for KX:Pb('2+) are well in accord with this model. / The angular dependence of the polarization of the A-band emission from KX:Pb('2+) confirms that the Pb('2+) - v(,c)('-) pair is located on the C(,4) crystallographic axis. The temperature dependence of the polarization is treated within the framework of the above model in terms of the nonradiative processes between the relaxed excited states.