An investigation was made at transonic speeds to determine some of the dynamic stability derivatives of a 45 deg. sweptback-wing airplane model. The model was sting mounted and was rigidly forced to perform a single-degree-of-freedom angular oscillation in pitch or yaw of /- 2 deg. The investigation was made for angles of attack alpha, from -4 deg. to 14 deg. throughout most of the transonic speed range for values of reduced-frequency parameter from 0.015 to 0.040 based on wing mean aerodynamic chord and from 0.04 to 0.14 based on wing span. The results show that reduced frequency had only a small effect on the damping-in-pitch derivative and the oscillatory longitudinal stability derivative for all Mach numbers M and angles of attack with the exception of the values of damping coefficient near M = 1.03 and alpha = 8 deg. to 14 deg. In this region, the damping coefficient changed rapidly with reduced frequency and negative values of damping coefficient were measured at low values of reduced frequency. This abrupt variation of pitch damping with reduced frequency was a characteristic of the complete model or wing-body-vertical-tail combination. The damping-in-pitch derivative varied considerably with alpha and M for the horizontal-tail-on and horizontal-tail-off configurations, and the damping was relatively high at angles of attack corresponding to the onset of pitch-up for both configurations. The damping-in-yaw derivative was generally independent of reduced frequency and M at alpha = -4 deg. to 4 deg. At alpha = 8 deg. to 14 deg., the damping derivative increased with an increase in reduced frequency and alpha for the configurations having the wing, whereas the damping derivative was either independent of or decreased with increase in reduced frequency for the configuration without the wing. The oscillatory directional stability derivative for all configurations generally decreased with an increase in the reduced-frequency parameter, and, in some instances, unstable values were measured for the model configuration with the horizontal tail removed.