In this work the authors study and extend the coding theory approach to error control in redundant residue number systems (RRNS). They derive new computionally efficient algorithms for correcting and detecting multiple errors and correcting single-burst errors. This paper is the continuation of Part I (see the preceding review) but it can be read in itself, too. The main results in this work are three computationally efficient procedures, which were presented in Sections IV, V and VI, respectively. These procedure for --- simultaneously correcting single errors and detecting multiple errors, --- simultaneously correcting double errors and detecting multiple errors, and --- correcting single-burst errors, are based on the generalized property of consistency checking for RRNS.