The evolving field of ear-mounted hearing devices manifests in more people wearing headphones, hearing aids or hearables in daily life. One of their purposes is to reduce the increasing burden of ambient noise. Their passive attenuation of noise can be supplemented by using Active Noise Cancellation (ANC). It uses acoustic anti-phase compensation. The occurring ambient noises in daily life can have a highly time-variant nature, e.g. with varying direction of arrival. In this contribution, we investi- gate the direction-dependency of ANC systems based on acoustic device-specific head related transfer functions (DHRTF). The DHRTF were measured with a fast measurement system for HRTF. We focus on in-ear headphones as the acoustic front-end. The headphones comprise two microphones; an outer microphone for ambient sounds and an inner microphone, which faces the eardrum. The transfer function between these two microphones is called the primary path. For the ANC system, we investigate optimal time-invariant feedforward filtering that depends on the primary path. Therefore, changes in the primary path due to varying directions of arrival may degrade the performance. The DHRTF measurements reveal differences in magnitude and phase of the primary path. Evaluations show that the attenuation per- formance depends on the direction of arrival.