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This paper presents two general fading distributions, the kappa-mu distribution and the eta-mu distribution, for which fading models are proposed. These distributions are fully characterized in terms of measurable physical parameters. The kappa-mu distribution includes the Rice (Nakagami-n), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. The eta-mu distribution includes the Hoyt (Nakagami-q), the Nakagami-m, the Rayleigh, and the one-sided Gaussian distributions as special cases. Field measurement campaigns were used to validate these distributions. It was observed that their fit to experimental data outperformed that provided by the widely known fading distributions, such as the Rayleigh, Rice, and Nakagami-m. In particular, the kappa-mu distribution is better suited for line-of-sight applications, whereas the eta-mu distribution gives better results for non-line-of-sight applications.