Quantum　walks　with　memory　(QWM)　are　types　of　modified　quantum　walks　that　record　the　walker＇s　latest　path.　The　general　model　of　coined　QWM　is　presented　in　Li　et　al.　(Phys　Rev　A　93:042323,　2016).　In　this　paper,　we　present　the　general　Szegedy　QWM　model　and　we　describe　its　relationship　with　the　coined　QWM　model.　A　coined　QWM　can　be　transformed　into　a　Szegedy　QWM,　while　a　Szegedy　QWM　can　be　transformed　into　a　coined　QWM　with　any　partition.　These　results　may　help　in　the　analysis　of　the　coined　QWM.　By　transforming　a　coined　QWM　into　a　Szegedy　QWM,　the　essential　structure　of　the　coined　QWM　is　revealed.　We　give　an　example　and　we　prove　that　two　known　QWMs　are　equal　when　they　have　a　proper　position-dependent　coin　operator.