A non-linear version of redundancy analysis is introduced. The technique is called REDUNDALS. It is implemented within the computer program for canonical correlation analysis called CANALS. The REDUNDALS algorithm is of an alternating least square (ALS) type. The technique is defined as minimization of a squared distance between criterion variables and weighted predictor variables. With the help of optimal scaling, the variables are non-linearly transformed. An application of the REDUNDALS technique used data from a survey conducted with members of the Dutch parliament who gave their opinions on seven issues and their preference votes for political parties. This example illustrates that the non-linear redundancy analysis corresponds to a multivariate multiple regression with optimal scaling. In the case of the Dutch parliamentary data, the REDUNDALS results are mostly comparable with the numerical CANALS analysis. The programs are combined, but CANALS finds directions in both sets of variables that correlate maximally, independent of how much variance is explained, while REDUNDALS explains as much variance as possible in every criterion direction. Two tables provide information about the parliamentary study, and a figure illustrates the monotone transformations of the variables. A 33-item list of references is included. (SLD)