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Multimodal biometric systems have consistently presented better recognition rates when compared to the unimodal systems that compose them. A common claim is that they also provide higher security when compared to unimodal systems since an intruder would have to successfully break into more than one biometrical system. We argue that this may not be true due to two main reasons: a multimodal system has a higher number of vulnerable points that may be explored by an intruder, and an intruder may break the multimodal system by attacking only a subset of the unimodal systems. In particular, we investigate a multimodal system composed of face and fingerprint under different spoof attack scenarios. In this case, a forger may choose to spoof the face or fingerprint traits. We empirically show that the false acceptance rate increases dramatically when either mode is spoofed, which means that an intruder may be falsely authenticated by spoofing only one mode.