A novel theoretical approach to the dynamics analysis of excitation and dephasing of plasmon modes in nanoparticles is presented. This approach is based on the biorthogonal plasmon mode expansion, and it leads to the predictions of time dynamics of excitation of specific plasmon modes as well as their steady state amplitude and their decay. Temporal characteristics of plasmon modes in nanoparticles are expressed in terms of their shapes, permittivity dispersion relations, and excitation conditions. In the case of the Drude model, analytical expressions for time-dynamics of plasmon modes are obtained.