This work presents the concept of Cascade Feature Selection to combine feature selection methods. Fast and weak methods, like ranking, are placed on the top of the cascade to reduce the dimensionality of the initial feature set. Thus, strong and computationally demanding methods, placed on the bottom of the cascade, have to deal with less features. Three cascade combinations are tested with the Extreme Learning Machine as the underlying classification architecture. The Tennessee Eastman chemical process simulation software and one high-dimensional data set are used as sources of the benchmark data. Experimental results suggest that the cascade arrangement can produce smaller final feature subsets, expending less time, with higher classification performances than a feature selection based on a Genetic Algorithm. Many works in the literature have proposed mixed methods with specific combination strategies. The main contribution of this work is a concept able to combine any existent method using a single strategy. Provided that the Cascade Feature Selection requirements are fulfilled, the combinations might reduce the time to select features or increase the classification performance of the classifiers trained with the selected features.