Abstract: The dissipative dynamics of a two-level system interacting with a reservoir has been solved by Markovian and non-Markovian approaches. The results in conditions of two different spectral densities, namely the detuning spectral density and a photonic gap distributed density, are compared with the exact solutions. In the first case, the population of excitation state in the non-Markovian and Markovian reservoirs is discussed. For both weak coupling regime in short time and a long period of strong coupling regime, the result of non-Markovian approaches is more consistent with the exact solution, while the Markovian approximation is mainly applicable to weak coupling condition. In the second case, the population in small gap width is considered. The Markovian approach is applied in weak coupling condition, but in strong condition the non-Markovian approximation is exploited. Therefore, through appropriate choice of Markovian and non-Markovian approaches, the dynamics of a system can be described exactly for different spectral densities and coupling regimes.