The basic properties of oblique anhysteretic remanent magnetization (OARM) acquired in a weak and steady magnetic field with an arbitrary angle to the alternating field direction were studied. OARM and rock-magnetic experiments were conducted on samples of basalt, granite, and sediment containing noninteracting single domain (SD), interacting SD, pseudo-single-domain, and multidomain low-Ti titanomagnetites. The intensity of OARM (M-OARM) systematically increased or decreased with increasing angle between alternating and steady field directions (theta(SF)), while the angle between alternating field and OARM directions (theta(OARM)) increased with increasing theta(SF) for all samples. During stepwise alternating field demagnetization, the OARM vector shows a single component parallel to the steady field direction for theta(SF)=0 degrees (ARM(parallel to)) and 90 degrees (ARM(perpendicular to)). The median destructive field of ARM is larger than that of ARM(parallel to). For intermediate angles (theta(SF)=30 degrees, 45 degrees, and 60 degrees), the OARM vector did not parallel the applied steady field but gradually increased theta(OARM) with higher coercivity. These experiments indicate that the OARM vector is approximately given by the sum of two orthogonal magnetizations coinciding with ARM(parallel to) and ARM(perpendicular to) respectively. Thus, the OARM vector can be determined by acquisition efficiencies of ARM(parallel to) and ARM(perpendicular to) in an individual sample. Based on these experiments and associated rock-magnetic measurements, noninteracting SD samples show lower ARM(perpendicular to)/ARM(parallel to) ratios, compared to other samples. This result suggests that OARM can be used as a useful tool to detect noninteracting SD particles in the paleomagnetic samples.