The estimation of the relative orders of the coefficients in the linear differential equations of longitudinal small perturbation of aircraft is used to analyse the classical simplified theory for the short- and long-period modes by the singular perturbation methods. The leading terms of the asymptotic expansions give the eigenvalues for short- and long-period modes with fairly good accuracy, except that the damping part of the eigenvalue for the long-period mode has relative error of the order of 10%. These approximate eigenvalues are improved by the method of strained co-ordinates which accounts for most of the differences. The dynamic response due to initial disturbances of velocity, angle of attack, and angle of pitch are also derived.