Face　recognition　for　surveillance　remains　a　complex　challenge　due　to　the　disparity　between　low-resolution　(LR)　face　images　captured　by　surveillance　cameras　and　the　typically　high-resolution　(HR)　face　images　in　databases.　To　address　this　cross-resolution　face　recognition　problem,　we　propose　a　two-stage　dual-resolution　face　network　to　learn　more　robust　resolution-invariant　representations.　In　the　first　stage,　we　pre-train　the　proposed　dual-resolution　face　network　using　solely　HR　images.　Our　network　utilizes　a　two-branch　structure　and　introduces　bilateral　connections　to　fuse　the　high-　and　low-resolution　features　extracted　by　two　branches,　respectively.　In　the　second　stage,　we　introduce　the　triplet　loss　as　the　fine-tuning　loss　function　and　design　a　training　strategy　that　combines　the　triplet　loss　with　competence-based　curriculum　learning.　According　to　the　competence　function,　the　pre-trained　model　can　train　first　from　easy　sample　sets　and　gradually　progress　to　more　challenging　ones.　Our　method　achieves　a　remarkable　face　verification　accuracy　of　99.25%　on　the　native　cross-quality　dataset　SCFace　and　99.71%　on　the　high-quality　dataset　LFW.　Moreover,　our　method　also　enhances　the　face　verification　accuracy　on　the　native　low-quality　dataset.　©　The　Author(s),　under　exclusive　licence　to　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature　2023.