We have considered the influence of electromagnetic fluctuations on electron tunneling via one nondegenerate resonant level, the problem that is relevant for electron transport through quantum dots in the Coulomb blockade regime. We show that the overall effect of the fluctuations depends on whether the electron bands in external electrodes are empty or filled. In the empty band case, depending on the relation between the tunneling rate \ensuremath{\Gamma} and characteristic frequency \ensuremath{\Omega} of the fluctuations, the field either simply shifts the conductance peak (for rapid tunneling, \ensuremath{\Gamma}\ensuremath{\gg}\ensuremath{\Omega}) or broadens it (for \ensuremath{\Gamma}\ensuremath{\ll}\ensuremath{\Omega}). In the latter case, the system can be in three different regimes for different values of the coupling g between electrons and the field. Increasing interaction strength in the region g1 leads to gradual suppression of the conductance peak at the bare energy of the resonant level ${\mathrm{\ensuremath{\varepsilon}}}_{0}$, while at g\ensuremath{\gg}1 it leads to the formation of a new peak of width ${\mathit{E}}_{\mathit{c}}$/${\mathit{g}}^{1/2}$ at the energy ${\mathrm{\ensuremath{\varepsilon}}}_{0}$+${\mathit{E}}_{\mathit{c}}$, where ${\mathit{E}}_{\mathit{c}}$ is a charging energy. For intermediate values of g the conductance is nonvanishing in the entire energy range from ${\mathrm{\ensuremath{\varepsilon}}}_{0}$ to ${\mathrm{\ensuremath{\varepsilon}}}_{0}$+${\mathit{E}}_{\mathit{c}}$. These results provide a possible explanation for the experimentally observed extra width of the conductance resonances at low temperatures. For filled bands the problem is essentially multielectron in character. One consequence of this is that, in contrast to the situation with the empty band, the fluctuations of the resonant level do not suppress conductance at resonance for g1. At gg1 the Coulomb gap appears in the position of the resonant level as a function of its bare energy, which leads to suppression of conductance.