Removing artifacts and background electroencephaloraphy (EEG) from multichannel interictal and ictal EEG has become a major research topic in EEG signal processing in recent years. We applied for this purpose a recently developed subspace-based method for modeling the common dynamics in multichannel signals. When the epileptiform activity is common in the majority of channels and the artifacts appear only in a few channels the proposed method can be used to remove the latter. The performance of the method was tested on simulated data for different noise levels. For high noise levels the method was still able to identify the common dynamics. In addition, the method was applied to real life EEG recordings containing interictal and ictal activity contaminated with muscle artifact. The muscle artifacts were removed successfully. For both the synthetic data and the analyzed real life data the results were compared with the results obtained with principal component analysis (PCA). In both cases, the proposed method performed better than PCA.