This paper considers power oscillation damping (POD) using active power modulation of high-voltage dc transmissions. An analytical study of how the proximity between interarea modal frequencies in two interconnected asynchronous grids puts a fundamental limit to the achievable performance is presented. It is shown that the ratio between the modal frequencies is the sole factor determining the achievable nominal performance. To illustrate the inherent limitations, simulations using a proportional controller tuned to optimize performance in terms of POD are done on a simplified two-machine model. The influence of limited system information and unmodeled dynamics is shown. The analytical result is then further validated on a realistic model with two interconnected 32-bus networks.