The direction-of-arrival (DOA) estimation problem consists in determining the angles of arrival of a number of signals impinging on a sensor array. Recently, the so-called ESPRIT method of Roy and Paulraj has received a great deal of attention in the literature. The method employs matrix decomposition techniques, such as singular value decomposition (SVD) and generalized Schur decomposition (GSD). The computational complexity thus involved represents a serious impediment, especially when a real-time implementation is aimed for. Therefore, the aim here is to develop an ESPRIT-type algorithm which is fully adaptive and amenable to parallel implementation. By introducing adaptivity, the computational complexity per sampling period is reduced from (Omicron) (m3) to (Omicron) (m2), where m is the `problem size,' i.e., the number of antenna doublets. On a parallel processor array with (Omicron) (m2) processors, the throughput is then (Omicron) (mo), which means that the number of measurements that are processed per time unit is independent of the problem size. The algorithm is based on an adaptive SVD updating algorithm, combined with an adaptive GSD. The corresponding systolic implementation is based on the systolic SVD updating array of Moonen et al.