In this paper, we present the system description of the joint efforts of Brno University of Technology (BUT) and Omilia — Conversational Intelligence for the ASVSpoof2019 Spoofing and Countermeasures Challenge. The primary submission for Physical access (PA) is a fusion of two VGG networks, trained on single and two-channels features. For Logical access (LA), our primary system is a fusion of VGG and the recently introduced SincNet architecture. The results on PA show that the proposed networks yield very competitive performance in all conditions and achieved 86\:\% relative improvement compared to the official baseline. On the other hand, the results on LA showed that although the proposed architecture and training strategy performs very well on certain spoofing attacks, it fails to generalize to certain attacks that are unseen during training.