The manual segmentation of individual retinal layers within optical coherence tomography (OCT) images is a time-consuming task and is prone to errors. The investigation into automatic segmentation methods that are both efficient and accurate has seen a variety of methods proposed. In particular, recent machine learning approaches have focused on the use of convolutional neural networks (CNNs). Traditionally applied to sequential data, recurrent neural networks (RNNs) have recently demonstrated success in the area of image analysis, primarily due to their usefulness to extract temporal features from sequences of images or volumetric data. However, their potential use in OCT retinal layer segmentation has not previously been reported, and their direct application for extracting spatial features from individual 2D images has been limited. This paper proposes the use of a recurrent neural network trained as a patch-based image classifier (retinal boundary classifier) with a graph search (RNN-GS) to segment seven retinal layer boundaries in OCT images from healthy children and three retinal layer boundaries in OCT images from patients with age-related macular degeneration (AMD). The optimal architecture configuration to maximize classification performance is explored. The results demonstrate that a RNN is a viable alternative to a CNN for image classification tasks in the case where the images exhibit a clear sequential structure. Compared to a CNN, the RNN showed a slightly superior average generalization classification accuracy. Secondly, in terms of segmentation, the RNN-GS performed competitively against a previously proposed CNN based method (CNN-GS) with respect to both accuracy and consistency. These findings apply to both normal and AMD data. Overall, the RNN-GS method yielded superior mean absolute errors in terms of the boundary position with an average error of 0.53 pixels (normal) and 1.17 pixels (AMD). The methodology and results described in this paper may assist the future investigation of techniques within the area of OCT retinal segmentation and highlight the potential of RNN methods for OCT image analysis.