In　this　paper　we　consider　some　reasons　for　the　occurrence　of　a　positive　near-anode　potential　drop　during　current　constriction　in　high-current　vacuum　arc.　It　is　shown　that　if　the　radius　of　constriction　is　much　larger　than　the　electron　mean　free　path,　then　a　positive　voltage　drop　in　the　near-anode　plasma　sheath　does　not　occur,　but　an　additional　drop　may　occur　in　the　near-anode　plasma　layer　due　to　the　anomalous　resistance.　If　the　current　constriction　radius　is　much　less　than　the　electron　mean　free　path,　then　a　positive　voltage　drop　in　the　sheath　arises　under　the　usual　condition,　and　the　kinetic　instabilities　in　the　near-anode　plasma　do　not　develop.　©　2019　IOP　Publishing　Ltd.　All　rights　reserved.