Parallel algorithms for multiple updating algorithms in recursive least-squares computations are investigated. Comparisons of updating algorithms by carefully implemented orthogonal Householder and Givens schemes are made on the iPSC hypercube distributed memory multiprocessor system. Overall, the performance of updating by orthogonal Householder reflections using a row-oriented storage scheme seems superior to those of Givens rotations using a row-oriented storage scheme and the greedy Givens sequence on the hypercube, for our application. In particular, the communication complexity is independent of the number of vectors being updated. The methods we describe can also be adapted to the parallel computation of general orthogonal factorizations involved in least-squares problems. We have in mind applications to windowed recursive least-squares filtering schemes for near real-time computations on distributed memory architectures.