The　concept　of　controlled　frames　is　a　generalization　of　that　of　frames,　It　has　important　application　in　solving　complicated　linear　systems.　This　paper　addresses　the　theory　of　controlled　continuous　g-frames.　Using　the　operator　methods,　we　establish　the　link　between　a　controlled　continuous　g-frame　and　a　continuous　g-frame,　and　obtain　their　induced　characterizations;　we　also　construct　new　controlled　continuous　g-frames　from　a　given　one.　Then,　we　give　some　identity　decompositions　of　controlled　continuous　g-frames.　Finally,　we　study　the　stabilities　of　controlled　continuous　g-frames　under　perturbations.　©　2021,　Chinese　Academy　of　Sciences.　All　right　reserved.