We study resonant tunneling through a single-level quantum dot in the presence of strong Coulomb repulsion beyond the perturbative regime. The level is either spin degenerate or can be split by a magnetic field. Furthermore we discuss the influence of a bosonic environment. Using a real-time diagrammatic formulation, we calculate transition rates, the spectral density, and the nonlinear I-V characteristic. The spectral density shows a multiplet of Kondo peaks split by the transport voltage and the boson frequencies and shifted by the magnetic field. This leads to zero-bias anomalies in the differential conductance, which agree well with recent experimental results for the electron transport through single-charge traps. Furthermore, we predict that the sign of the zero-bias anomaly depends on the level position relative to the Fermi level of the leads.© 1996 The American Physical Society.