Two iterative algorithms are formulated for the solution of the within-group neutron diffusion equation in three dimensions. The algorithms are highly vectorizable, operating, respectively, on vectors with lengths of order N3/2 and of N2/2, where N is the number of mesh points in each of the three directions. The methods are well suited for present day pipeline computers. On a Cyber-205, they yield floating point operation rates that are higher by a factor of 20 to 30 than those achieved with scalar operations of the same algorithms. Convergence rates, as well as acceleration by two-cyclic overrelaxation, are investigated. For fixed source test problems with 30 X 30 X 30 grids, solutions are obtained in ∼1 s.