The automatic speaker verification system is sometimes vulnerable to various spoofing attacks. The 2-class Gaussian Mixture Model classifier for genuine and spoofed speech is usually used as the baseline for spoofing detection. However, the GMM classifier does not separately consider the scores of feature frames on each Gaussian component. In addition, the GMM accumulates the scores on all frames independently, and does not consider their correlations. We propose the two-path GMM-ResNet and GMM-SENet models for spoofing detection, whose input is the Gaussian probability features based on two GMMs trained on genuine and spoofed speech respectively. The models consider not only the score distribution on GMM components, but also the relationship between adjacent frames. A two-step training scheme is applied to improve the system robustness. Experiments on the ASVspoof 2019 show that the LFCC+GMM-ResNet system can relatively reduce min-tDCF and EER by 76.1% and 76.3% on logical access scenario compared with the GMM, and the LFCC+GMM-SENet system by 94.4% and 95.4% on physical access scenario. After score fusion, the systems give the second-best results on both scenarios.