Sclera segmentation is an important processing step in a biometric system based on this modality. We propose adaptations of five deep neural network architectures: SegNet, DeepLabv3+, HRNetV2, UPerNet, and U-Net for sclera segmentation. The architectures are experimentally evaluated on recent MASD and SBVPI eye image datasets using standard metrics: precision, recall, F_1-score and intersection over union. Experiments on the SBVPI dataset show that the performance for sclera segmentation of the five deep neural network architectures is very similar in terms of the used metrics and acceptable for practical applications. Additionally, the SegNet, HRNetV2 and UPerNet, and U-Net tested on MASD perform better in the terms of precision metrics than the winning U-Net adaptation from the Sclera Segmentation Benchmark Competition 2019 (SSBC 2019), with our U-Net being the best deep model.