The smoothing problem for discrete-time gaussian reciprocal processes is examined. For this class of process, the smoother takes the form of a second-order two-point boundary-value nearest-neighbour model. This smoother is non-causal, but admits causal implementations which extend the two-filter and Rauch-Tung-Striebel smoothing formulae of Gauss-Markov processes. A multi-rate implementation based on a block cyclic reduction method is also described.