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Deepfakes represent the generation of synthetic/fake images or videos using deep neural networks. As the techniques used for the generation of deepfakes are improving, the threats including social media disinformation, defamation, impersonation, and fraud are becoming more prevalent. The existing deepfakes detection models, including those that use convolution neural networks, do not generalize well when subjected to multiple deepfakes generation techniques and cross-corpora setting. Therefore, there is a need for the development of effective and efficient deepfakes detection methods. To explicitly model part-whole hierarchical relationships by using groups of neurons to encode visual entities and learn the relationships between real and fake artifacts, we propose a novel deep learning model efficient-capsule network (E-Cap Net) for classifying the facial images generated through different deepfakes generative techniques. More specifically, we introduce a low-cost max-feature-map (MFM) activation function in each primary capsule of our proposed E-Cap Net. The use of MFM activation enables our E-Cap Net to become light and robust as it suppresses the low activation neurons in each primary capsule. Performance of our approach is evaluated on two standard, largescale and diverse datasets i.e., Diverse Fake Face Dataset (DFFD) and FaceForensics++ (FF++), and also on the World Leaders Dataset (WLRD). Moreover, we also performed a cross-corpora evaluation to show the generalizability of our method for reliable deepfakes detection. The AUC of 99.99% on DFFD, 99.52% on FF++, and 98.31% on WLRD datasets indicate the effectiveness of our method for detecting the manipulated facial images generated via different deepfakes techniques.