By using a three-dimensional fully nonlinear numerical model in spherical coordinates and taking the linear steady solutions of the migrating diurnal and semidiurnal tides in January from the Global-Scale Wave Model (GSWM) as the initial values, we simulate the linear and nonlinear propagations of the migrating diurnal and semidiurnal tides in the atmosphere from the ground to the lower thermosphere. A comparison of our simulations with the results of GSWM is also presented. The simulation results show that affected by the nonlinearity, the migrating diurnal and semidiurnal tides propagating in the middle and upper atmosphere exhibit evident short-term variability. The nonlinear interactions between the migrating tides and the background atmosphere can obviously alter the background wind and temperature fields, which suggests that the nonlinear propagations of the migrating diurnal and semidiurnal tides impact significantly on the transient dynamical and thermal structures of the background middle and upper atmosphere and the nonlinear effect is an important cause of the difference between the results of GSWM and observations.