Two error-correcting algorithms for redundant residue number systems are presented, one for single residue-error correction and the other for burst residue-error correction. Neither algorithm requires table lookup, and hence their implementation needs a memory space which is much smaller than that required by existing methods. Furthermore, the conditions which the moduli of the redundant residue number systems must satisfy for single residue-error correction are less restrictive than that of existing methods. Comparison of the approach on which these two algorithms are based and that of existing methods is given.