The peculiar behavior of Kondo-peak splitting under a magnetic field and bias can be explained by calculating the nonequilibrium retarded Green's function via the nonperturbative dynamical theory (NDT). In the NDT, the application of a lead-dot-lead system reveals that new resonant tunneling levels are activated near the Fermi level and the conventional Kondo peak at the Fermi level diminishes when a bias is applied. Magnetic field causes asymmetry in the spectral density and transforms the new resonant peak into a major peak whose behavior explains all the features of the nonequilibrium Kondo phenomenon. We also show the mechanism of coherent transport through the new resonant tunneling level.