In an azimuth/inclination-angle detection apparatus, a measurement data obtaining unit obtains first and second measurement data sets g and h from acceleration and magnetic sensors, respectively. A first computation unit calculates an azimuth α0, an elevation angle β0, and a geomagnetism depression angle θ0 from the measurement data sets g and h. An averaging unit accumulates and averages the geomagnetism depression angle θ0 so as to obtain a value to be used as a geomagnetism depression angle θ. A second computation unit calculates an azimuth α and an elevation angle β from the second measurement data set h and the geomagnetism depression angle θ. When a plurality of solutions exist, they are stored as candidates (α1, β1) and (α2, β2). A selection unit selects a detection value (α, β) from the candidates (α1, β1) and (α2, β2) with reference to the above-described values α0 and β0 serving as reference values.