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The task of logo detection is desirable and important for various fields. However, it is challenging and difficult to identify logos in complex scenarios as a logo can appear in different styles and platforms. Logo images include diverse contexts, sizes, projective transformation, resolution, illumination and fonts, which make it more difficult to detect a logo. To address these issues, we presented a deep learning-based algorithm for logo detection called LogoNet. It includes an hourglass like top-down bottom-up feature extraction network, a spatial attention module and an anchorfree detection head similar to CenterNet. In order to improve performance, in this paper, an extended version of LogoNet is proposed, called—Dual-Attention LogoNet, that exploits different attention mechanisms more efficiently. The incorporated channel-wise and spatial attention modules refine and generate robust and balanced feature maps to predict visual and semantic information more accurately. In addition, we propose a lightweight architecture for both LogoNet and Dual-Attention LogoNet for practical applications. The proposed lightweight architecture significantly reduces the number of network parameters and improves the inference time to address the real-time performance while maintaining accuracy. Furthermore, to address the domain shift problem in practical applications, we also propose an adversarial-learning-based domain adaptation approach, which is easily adaptable to any anchorfree detectors. Our attention-based method shows a 1.8% improvement in accuracy compared to the state-of-the-art detection network on the FlickrLogos-32 dataset. Our proposed domain adaptation approach significantly improves performance by 1.3% mAP compared to direct transfer on the target domain without increasing any labeling cost and network parameters.