The　minimum　codegree　threshold　for　a　perfect　matching　in　a　k-graph　with　n　vertices　was　determined　by　Rodl,　Rucinski,　and　Szemeredi　for　the　case　when　n　equivalent　to　0　(mod　k).　Recently,　Han　resolved　the　remaining　cases　when　n　not　equivalent　to　0　(mod　k),　establishing　a　conjecture　of　Rodl,　Rucinski,　and　Szemeredi.　In　this　paper,　we　determine　the　minimum　codegree　threshold　for　almost　perfect　matchings　in　k-partite　k-graphs,　answering　a　question　of　Rodl　and　Rucinski.