Abstract: A new theory for studying temporal aberrations of dynamic electron optical imaging systems by the direct integral method（DIM） is put forward.A new definition of temporal aberration is given taking a certain initial energy of electron emission emitted from the cathode surface along the axial direction ε_z1(0≤ε_z1≤ε_0max) as a criterion.New expressions of the temporary aberration coefficients expressed in integral forms for the dynamic electron optical imaging system are deduced.An electrostatic concentric spherical system model is used to test and verify the expressions of temporal aberrations given by DIM and the τ-variation method,the analytical solutions prove that both of the two methods are correct and equivalent.Compared to the τ-variation method,DIM needs only to carry out the integral calculation for the three of temporal geometrical aberration coefficients of second order,and is therefore more convenient and suitable for computation in practical design operations.Finally,what we have learned from the study of the theory of temporal aberrations for dynamic electron optics from the point of view of methodology was elaborated.