Let　G1　and　GI　be　two　connected　graphs.　The　Kronecker　product　G\　x　GI　has　vertex　set　V{G1　x　G2)　=　V{G1)　x　V(G2)　and　the　edge　set　E(G1　x　G2)　=　{(u1　,　v1)(U2,V2)　:　u1u2　€　E(GI),V1V2　€=　E(G2)}-　Let　S　⊆　V　be　a　vertex　set,　S　is　called　h-extra　cut,　if　G-　S　is　not　connected　and　each　component　oiG-S　has　more　than　h　vertices.　The　h-extra　connectivity　Kh(G)　is　the　cardinality　of　the　minimum　/i-extra　cuts.　In　this　paper,　we　determine　the　h-ex　tra　connectivity　of　Km　X　Kn,　Km　x　Pn　and　Km　X　Cn.　©　2018　Charles　Babbage　Research　Centre.　All　rights　reserved.