An ever-increasing number of data analysis problems include more than one view of the data, i.e. differ- ent measurement approaches to the population under study. In consequence, pattern analysis methods that deal appropriately with multiview data are becoming increasingly useful. In this paper, a novel mul- tiview spectral clustering algorithm is presented (multiview spectral clustering by common eigenvectors, or MVSC-CEV), based on computing the common eigenvectors of the Laplacian matrices derived from the similarity matrices of the input data. This algorithm maintains the features of spectral clustering, while allowing the use of an arbitrary number of input views, possibly of a different nature (feature or graph space) and with different dimensions. The method has been tested on four standard multiview data sets (UCI’s Handwritten, BBC segmented news, Max Planck Institute’s Animal With Attributes and Reuters multilingual), and compared with seven methods in the state of the art. Seven standard clus- tering evaluation metrics have been used in the experiments. The quality of the clustering produced by MVSC-CEV is above those obtained by other state-of-the-art methods in the majority of evaluation met- rics and dataset combinations. The computation times of this method are approximately twice those of the baseline spectral clustering of the concatenated data views.