Immune checkpoint inhibitors (ICI) represent a new therapeutic approach in recurrent and metastatic head and neck squamous cell carcinoma (HNSCC). The patient selection for the PD-1/PD-L1 inhibitor therapy is based on the degree of PD-L1 expression in immunohistochemistry reflected by manually determined PD-L1 scores. However, manual scoring shows variability between different investigators and is influenced by cognitive and visual traps and could therefore negatively influence treatment decisions. Automated PD-L1 scoring could facilitate reliable and reproducible results. Our novel approach uses three neural networks sequentially applied for fully automated PD-L1 scoring of all three established PD-L1 scores: tumor proportion score (TPS), combined positive score (CPS) and tumor-infiltrating immune cell score (ICS). Our approach was validated using WSIs of HNSCC cases and compared with manual PD-L1 scoring by human investigators. The inter-rater correlation (ICC) between human and machine was very similar to the human-human correlation. The ICC was slightly higher between human-machine compared to human-human for the CPS and ICS, but a slightly lower for the TPS. Our study provides deeper insights into automated PD-L1 scoring by neural networks and its limitations. This may serve as a basis to improve ICI patient selection in the future.