The usual technique of longitudinal stability analysis is adopted but particular attention is paid to those elements that contribute to damping, The cases of two delta plan form. aircraft of 45° and 60° sweep angle are considered and, in the light of the best available data, their derivatives and the coefficients of the stability- quartics are obtained for a range of Mach numbers including the transonic range. An analysis is made of the damping of the short period oscillation in each case and this is compared with a requirement to damp to half-amplitude in less than one cycle. The results are dependent on estimates and assumptions that cannot be regarded as completely reliable in the absence of experimental data, and quasi-static derivatives are used in cases where frequency effects should properly be included; but the broad implications of the results are probably acceptable.