Procedure step recognition (PSR) aims to identify all correctly completed steps and their sequential order in videos of procedural tasks. The existing state-of-the-art models rely solely on detecting assembly object states in individual video frames. By neglecting temporal features, model robustness and accuracy are limited, especially when objects are partially occluded. To overcome these limitations, we propose Spatio-Temporal Occlusion-Resilient Modeling for Procedure Step Recognition (STORM-PSR), a dual-stream framework for PSR that leverages both spatial and temporal features. The assembly state detection stream operates effectively with unobstructed views of the object, while the spatio-temporal stream captures both spatial and temporal features to recognize step completions even under partial occlusion. This stream includes a spatial encoder, pre-trained using a novel weakly supervised approach to capture meaningful spatial representations, and a transformer-based temporal encoder that learns how these spatial features relate over time. STORM-PSR is evaluated on the MECCANO and IndustReal datasets, reducing the average delay between actual and predicted assembly step completions by 11.2% and 26.1%, respectively, compared to prior methods. We demonstrate that this reduction in delay is driven by the spatio-temporal stream, which does not rely on unobstructed views of the object to infer completed steps. The code for STORM-PSR, along with the newly annotated MECCANO labels, is made publicly available at https://timschoonbeek.github.io/stormpsr .