Experimental data from two Yb3+, Er3+ :yttrium aluminum garnet (YAG) crystal samples with different doping concentrations were analyzed through the calculation of the exact solution of the general nonradiative energy-transfer master equations. Besides the dipole-dipole direct energy transfer and the dipole-dipole migration processes assumed by other authors to predict the Yb3+-fluorescence decay, it is shown that a quadrupole-quadrupole direct energy transfer and a dipole-dipole back-transfer process are also present. The used free parameter values predicted our experimental data as well as other experimental data reported in the literature. Further, our modeling also calculates the acceptor transients which were also compared to experimental data. Therefore, the used modeling can be applied to analyze complicated nonradiative energy-transfer processes where traditional models fail.