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The performance of a Convolutional Neural Network (CNN) highly depends on its architecture and corresponding parameters. Manually designing a CNN is a time-consuming process in regards to the various layers that it can have, and the variety of parameters that must be set up. Increasing the complexity of the network structure by employing various types of connections makes designing a network even more challenging. Evolutionary computation as an optimisation technique can be applied to arrange the CNN layers and/or initiate its parameters automatically or semi-automatically. Dense network and Residual network are two popular network structures that were introduced to facilitate the training of deep networks. In this paper, leveraging the potentials of Dense and Residual blocks, and using the capability of evolutionary computation, we propose an automatic evolutionary model to detect an optimum and accurate network structure and its parameters for medical image segmentation. The proposed evolutionary DenseRes model is employed for segmentation of six publicly available MRI and CT medical datasets. The proposed model obtained high accuracy while employing networks with minimal parameters for the segmentation of medical images and outperformed manual and automatic designed networks, including U-Net, Residual U-Net, Dense U-Net, Non-Bypass Dense, NAS U-Net, AdaresU-Net, and EvoU-Net.