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CNN architectures are generally heavy on memory and computational requirements which makes them infeasible for embedded systems with limited hardware resources. We propose dual convolutional kernels (DualConv) for constructing lightweight deep neural networks. DualConv combines 3$\times$3 and 1$\times$1 convolutional kernels to process the same input feature map channels simultaneously and exploits the group convolution technique to efficiently arrange convolutional filters. DualConv can be employed in any CNN model such as VGG-16 and ResNet-50 for image classification, YOLO and R-CNN for object detection, or FCN for semantic segmentation. In this paper, we extensively test DualConv for classification since these network architectures form the backbones for many other tasks. We also test DualConv for image detection on YOLO-V3. Experimental results show that, combined with our structural innovations, DualConv significantly reduces the computational cost and number of parameters of deep neural networks while surprisingly achieving slightly higher accuracy than the original models in some cases. We use DualConv to further reduce the number of parameters of the lightweight MobileNetV2 by 54% with only 0.68% drop in accuracy on CIFAR-100 dataset. When the number of parameters is not an issue, DualConv increases the accuracy of MobileNetV1 by 4.11% on the same dataset. Furthermore, DualConv significantly improves the YOLO-V3 object detection speed and improves its accuracy by 4.4% on PASCAL VOC dataset.