Orientation of the weak biasing field obliquely, rather than parallel, to the strong alternating field causes an oblique anhysteretic remanent magnetization (OARM) which is systematically misaligned with respect to the bias. Experiments on a deep-sea sediment also showed that with increasing bias angle the intensity of OARM diminishes greatly, the coercive force is slightly lower, and the remanence is monodirectional over all coercive force bands. An adaptation of the Stoner-Wohlfarth mechanism described here may help to explain some fundamental aspects of OARM behavior.