Two methods of augmenting the structure of a sequential machine so that it is diagnosable are presented. The checkable (checking sequences) and repeated symbol distinguishing sequences (RDS) are discussed. It was found that as few as twice the number of outputs of the given machine is sufficient for constructing a state-output augmentation with RDS. Techniques for minimizing the number of states in resolving convergences and in resolving equivalent and nonreduced cycles are developed