Case-based reasoning (CBR) is a problem solving approach that uses past experience to tackle current problems. CBR has demonstrated to be appropriate for working with unstructured domains data or difficult knowledge acquisition situations, as it is the case of the diagnosis of many diseases. Some of the trends and opportunities that may be developed for CBR in the health science are oriented to reduce the number of features in highly dimensional data, as well as another important focus on how CBR can associate probabilities and statistics with its results by taking into account the concurrence of several ailments. In this paper, in order to adequately represent the database and to avoid the inconveniences caused by the high dimensionality, a number of algorithms are used in the preprocessing stage for performing both variable selection and dimension reduction procedures. Subsequently, we make a comparative study of multi-class classifiers. Particularly, four classification techniques and two reduction techniques are employed to make a comparative study of multi-class classifiers on CBR.