We report an experimental investigation of the structure of the wake and oscillation dynamics of gas-liquid compound drops rising at high Reynolds numbers. Particle image velocimetry (PIV) and high-speed shadowgraph techniques were used to determine the conditions required for the motion to become unstable and to gain insight into the origin of the instability. Three combinations of fluids were tested for a wide range of the diameter ratio db/dcd - i.e., the equivalent diameter of the gas bubble divided by that of the liquid layer -, while the Reynolds number spans roughly from 200 to 700. As db/dcd is increased beyond a critical range, the flow becomes unstable. The compound drops follow a pendular oscillation where the centroid of the liquid acts as a pivot with respect to the top of the compound drop, whose dynamics depends greatly on db/dcd. Measurements of the normal and streamwise vorticities pointed to the instability of the wake as the origin of the oscillation, similarly to a rigid sphere. However, the multiphase structure of the drop also contributed to the destabilization of the system, shifting the motion transition to a lower Reynolds number. The pendular oscillation favors the asymmetry of the flow field behind the compound drop, amplifying the unsteadiness of the wake. The induced path oscillation is therefore shown to result from the coupling of the wake vortex detachment and the pendulum motion induced by the sloshing of the liquid layer inside the compound drop.