Recently,　there　has　been　increasing　interest　in　the　Source-Free　Domain　Adaptive　Object　Detection　task,　which　involves　training　an　object　detector　on　the　unlabeled　target　data　using　a　pre-trained　source　model　without　accessing　the　source　data.　Most　related　methods　are　developed　from　the　mean-teacher　framework,　which　aims　to　train　the　student　model　closer　to　the　teacher　model　via　a　pseudo　labeling　manner,　where　the　teacher　model　is　the　exponential-moving-average　of　the　student　models　at　different　time-steps.　Following　this　line　of　works,　we　propose　a　Run-and-Chase　Mutual-Learning　method　to　strengthen　the　interactions　between　the　student　model　and　the　teacher　model　in　both　feature　and　prediction　levels.　In　our　method,　the　student　model　is　optimized　to　run　away　from　the　teacher　model　at　the　feature　level,　while　chasing　the　teacher　model　at　the　prediction　level.　In　this　way,　the　student　model　is　forced　to　be　distinguishable　at　different　time-steps,　so　that　the　teacher　model　can　acquire　more　diverse　task-related　information　and　produce　higher-accuracy　pseudo　labels.　As　the　training　goes,　the　student　and　teacher　models　are　updated　iteratively　and　promoted　mutually,　which　can　prevent　the　model　collapse　problem.　Extensive　experiments　are　conducted　to　validate　the　effectiveness　of　our　method.　©　2023　IEEE.