At least squares mathematical modeling technique is used to analyze af step demagnetization data of an individual rock specimen. Its total magnetization is separated to give the directions, magnitudes, and decay rates of the inherent magnetization components. An estimate of the uncertainty in the directions and magnitudes of the components is also computed. The method assumes that the direction of each component remains constant as its intensity decreases approximately exponentially during demagnetization. Two tests comparing the mean directions determined by using the af demagnetization data of a single specimen per site to those determined by using traditional paleomagnetic analysis of multiple demagnetized specimens per site given identical results at the 95% confidence level.