|Face morphing attacks are verifiable to multiple identities, leading to faulty identity links. Recent works have studied the face morphing attack detection performance over variations in morphing approaches, pointing out low generalization. This work studies detecting these attacks as anomalies and discusses the performance and generalization over different morphing types. We also analyze the accuracy and generalization effect of including different amounts of attack contamination in the anomaly training data (novelty vs. outlier). This is performed with two baseline 2-class classifiers, two approaches for anomaly detection, two image feature extractions, two morphing types, and variations in contamination levels and tolerated training errors. The results points out the relative lower performance, but higher generalization ability, of anomaly detection in comparison to 2-class classifiers, along with the benefits of contaminating the anomaly training data.