In this paper, we explore the use of novel neural-network architectures to distinguish natural seepages from artificial slicks in Synthetic Aperture Radar (SAR) images. They exploit a distinctive property of natural seepages, which is their temporal recurrence in the same geographical area. This information can be captured in different SAR images acquired at the same location over time, but not necessarily at a regular time-frequency. The proposed neural-network architectures are then built as specific block layers, which efficiently treat the unordered temporal information, followed by more conventional neural-network layers, which are widely used for image classification. Different block layers for unordered temporal information are compared on Sentinel-1 images acquired in the Aegean Sea. Following data augmentation steps, our dataset contains a consistent subset of images gathered among 16000 time-patches. We demonstrate that non-linear time-based block layers and block layers that avoid information bottlenecks are most efficient to discriminate between natural and artificial oil spills. Compared with standard neural-networks which use single time-frames, the integration of unordered temporal information increases the overall accuracy (OA) from 82% to 92% on our dataset, which demonstrates the effectiveness of the proposed approach.