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A general description of the dynamics of nonequilibrium carriers in multicomponent activated scintillation materials with a compositional disorder of the crystalline matrix is developed and applied for studying the excitation transfer and timing properties of lutetium–yttrium oxyorthosilicate (LYSO). The energy structure, the density of states, and the effective potential of LSO and YSO crystals have been calculated by using the Quantum Espresso package. An analytical form of the potential fluctuations due to compositional disorder is suggested in the pseudopotential approximation. The spatial distribution of lutetium and yttrium cations in the LYSO crystal has been simulated by the Monte Carlo method using the thermodynamic approach for three qualitatively different cases of cation distribution: uniform, heterogeneous neighboring, and clustered. The impact of the compositional disorder on electron migration is found to be qualitatively different in four typical regions of electron energy. The density of localized states in LYSO calculated using the coherent potential approximation (CPA) and the quasiclassical approach is comparable to the density of secondary carriers expected in an ionization track and might have significant influence on the migration of thermalized carriers. The transport mean free path of nonlocalized electrons limited by elastic scattering on pseudopotential fluctuations is shown to be substantially longer than that due to longitudinal optical phonon emission in the low-energy region (calculated using CPA) and the high-energy region (calculated using the Born approximation). The scattering on pseudopotential fluctuations is important for intermediate-energy electrons due to a substantial influence of the core potential fluctuations on high-energy branches. [ABSTRACT FROM AUTHOR]