In this paper we describe algorithms for solving nonlinear least-squares problems on a message-passing multiprocessor. We demonstrate new parallel algorithms, including an efficient parallel algorithm for determining the Levenberg-Marquardt parameter and a new row-oriented QR factorization algorithm. Experimental results obtained on an Intel iPSC hypercube are presented and compared with sequential MINPACK code executed on a single processor. These experimental results show that essentially full efficiency is obtained for problems where the row size is sufficiently larger than the number of processors. These algorithms have the advantage of involving only simple data movements and consequently are not constrained to the hypercube architecture.