This paper investigates how to solve image classification with Hopfield neural networks (HNNs) and oscillatory neural networks (ONNs). This is a first attempt to apply ONNs for image classification. State-of-the-art image classification networks are multi-layer models trained with supervised gradient back-propagation, which provide high-fidelity results but require high energy consumption and computational resources to be implemented. On the contrary, HNN and ONN networks are single-layer, requiring less computational resources, however, they necessitate some adaptation as they are not directly applicable for image classification. ONN is a novel brain-inspired computing paradigm that performs low-power computation and is attractive for edge artificial intelligence applications, such as image classification. In this paper, we perform image classification with HNN and ONN by exploiting their auto-associative memory (AAM) properties. We evaluate precision of HNN and ONN trained with state-of-the-art unsupervised learning algorithms. Additionally, we adapt the supervised equilibrium propagation (EP) algorithm to single-layer AAM architectures, proposing the AAM-EP. We test and validate HNN and ONN classification on images of handwritten digits using a simplified MNIST set. We find that using unsupervised learning, HNN reaches 65.2%, and ONN 59.1% precision. Moreover, we show that AAM-EP can increase HNN and ONN precision up to 67.04% for HNN and 62.6% for ONN. While intrinsically HNN and ONN are not meant for classification tasks, to the best of our knowledge, these are the best-reported precisions of HNN and ONN performing classification of images of handwritten digits.