A method for investigation of stability of rolling aircrafts of inertially slender configuration is introduced. It includes the monotonic dependence of lateral-directional derivatives upon angle of attack, which is called "Aerodynamic cross-coupling", and expressed by the derivatives (Cl Cl , Cl6a04' Cn and 0c4 rot 1:20' Cnoacx). An application to a supersonic fighter model is made, in order to emphasize the effect of aerodynamic cross-coupling upon values and stability of pseudosteady roll rates. When results were compared with that obtained by neglecting aerodynamic cross-coupling, it was found that, the stable linear part of response is enlarged and the critical unstable area is completely disappeared. The results of the method were supported by a time domain simulation of the complete nonlinear equations of motion, beside a detailed analysis. Generally, it could be concluded that, the consideration of aerodynamic cross-coupling adds a source of nonlinearity to the response of a rolling aircraft, which may varry the stability margins provided, specially at
large aileron deflections.